untitled - school of mathematical & computer sciences - heriot-watt

Contents

Page

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

Degrees Offered . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

The Mentor System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

Professional Development & Career Advice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

Notification of Special Circumstances . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

Computing Facilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

Academic Staff . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

University Prizes & Bursaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .7

Exchange Opportunities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

Industrial Placements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

Course & Examination Requirements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

Plagiarism & Cheating . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

Course Information

Course Structure & Assessment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

1st Year Courses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .10

2nd Year Courses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .11

3rd Year Courses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

4th Year Courses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

Actuarial Exemptions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

Miscellaneous . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

AMS Course Descriptions

Level 7 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

Level 8 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

Level 9 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

Level 10/11 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .29

2

INTRODUCTION

This guide provides a reference to degree programme structures and other departmen-tal information for students on Actuarial Mathematics and Statistics (AMS) degrees. Itshould be read and used in conjunction with the Undergraduate Programme Handbook forThe School of Mathematical and Computer Sciences (MACS Guide) which contains moredetailed information on University Regulations and procedures. This guide is intendedas a summary of AMS Programme Structures, but note that the University Regulationsand Programme Structures take precedence in case of any discrepancy between them andthe guide. Information concerning term dates, examination timetables, University reg-ulations and other general information can be found on the Academic Registry websiteat www.hw.ac.uk/registry/. A further source of information is the MACS web site atwww.macs.hw.ac.uk/home.

DEGREES OFFERED

The following undergraduate degrees, which may be awarded at honours or ordinary level,are offered:

F713. B.Sc. in Statistical ModellingF723. B.Sc. in Actuarial ScienceF771. B.Sc. in Financial Mathematics.

Study for an honours degree usually takes four years, and for an ordinary degree, threeyears.

All the degrees are designed to make it easy in most cases to transfer from one to anotherduring the first two years. In addition, the Heriot-Watt course scheme is compliant withthe Scottish Credit and Qualifications Framework (SCQF). This makes credit transfersbetween Scottish universities easier.

3

THE MENTOR SYSTEM

You will be allocated a mentor when you arrive at the University and, normally, you willretain the same mentor as long as you are registered on an AMS degree. The mentoris your main academic link with the University. Under certain circumstances, with thepermission of the Head of AMS, it may be possible to change your mentor.

Regular Meetings

It is important that you see your mentor regularly. These meetings are particularly impor-tant for monitoring academic progress in the first and second years. All students must seetheir mentors at the start of Semester 1 and week 4 of Semester 2. In addition, first andsecond year students must see their mentors in week 7 of Semester 1 and week 8 of Semester2. Mentors often arrange meetings via e-mail, or post notices on their office doors. It isyour responsibility to find out what arrangements have been made. In particular, you areexpected to check your e-mail regularly (at least once a week) and to ensure thatyour in-box is regularly cleared.

Help & Advice

Every year a few students run into serious personal difficulties (e.g. family illness, accom-modation, financial, etc.). As well as being generally supportive, mentors can help in anumber of practical ways. For example, if you are prevented from completing project workor sitting exams, your mentor can sometimes help with re-scheduling or making alternativearrangements for assessment. However, you must notify your mentor as soon as possible,or there is very little that can be done. This is particularly important if the difficultyaffects your sitting Level 9 or 10 honours papers, as once taken there are no resits allowedfor honours papers. Also, it is essential to submit a Special Circumstances Form (seeNotification of Special Circumstances, p5). With other problems, your mentor canput you in touch with the appropriate University support service (Chaplaincy, MedicalCentre, Student Welfare Services or Student Union). The mentors are there to help; donot hesitate to contact yours if you need help.

Staff-Student Committee

The Staff-Student Committee provides an additional channel of communication betweenstaff and students within the AMS department. It consists of the School Officer, theDirectors of Study, and two student representatives from each of the four undergraduateyears. Student representatives are elected annually.

The committee meets twice each term. One of its major functions is to consider anyconcerns about current lecture courses, including teaching quality, and to take appropriateaction for their resolution. Other matters of interest, such as the provision of computingfacilities or the timing of lectures, may be discussed. Minutes of the meetings are postedon the noticeboard outside CMS.01.

4

PROFESSIONAL DEVELOPMENT & CAREERS ADVICE

Professional development planning (PDP) is incorporated in all four years of the AMSdegrees. This is a structured process designed to help students reflect upon their ownlearning, performance and achievements. One of its main purposes is to support studentsin the planning of their professional, educational and careers development. In addition totaking a PDP course in 1st year, students will periodically attend seminars on developingthese skills, given by, for example, prospective employers. In later years, there will be op-portunities to develop presentation and group skills. Career guidance is available throughthe University’s Careers Advisory Service, which gives a number of presentations on topicsrelated to careers. Students are encouraged contact Mr A. Smith there for advice. Withinthe AMS department, Mr G. Reid is also able to provide some information.

NOTIFICATION OF SPECIAL CIRCUMSTANCES

If there are any special circumstances, such as illness or the death of a close relative,which could adversely affect your examination performance, it is very important that younotify your mentor as soon as possible. A Special Circumstances Form (obtainable fromthe MACS Office or the Registry website www.hw.ac.uk/registry/forms.html), togetherwith any supporting documents (e.g. medical certificates), must also be submitted to theMACS Office (EM 1.25). The Examiners will always take such circumstances into accountwhere appropriate, but the later the notification, the less scope there is to do so. Inparticular, notification should be before the examination diet concerned, and certainly nolater than the Examiners Meeting (usually at the end of the assessment period, or lateAugust in the case of re-sits). Late notification will mean that either no account can betaken, or that formal procedures have to be invoked. In the latter case, final year studentswill not be permitted to graduate until these procedures have been completed. For furtherdetails, see the MACS Guide and the University Regulations.

COMPUTING FACILITIES

All AMS students are issued with accounts on the University Desktop Service. For detailsof computer lab locations and availability, see www.hw.ac.uk/it/Guide to Services/pclablocations.html. Students are expected to use the computing facilities in an ap-propriate and considerate way. Abuse of the facilities is subject to various disciplinarymeasures, ranging from a ban on access to the facilities to, in extreme and flagrantcases, expulsion from the University. Examples of abuse include monopolising a termi-nal for non-academic related purposes, running excessively long or inappropriate printjobs, and displaying, circulating or printing offensive material on or from the internet.Computer games and relay chat are specifically forbidden. Further information on policyregarding the abuse of computing facilities is available from Information Technology (IT)www.hw.ac.uk/it/Rules Regulations/index.html.

5

ACADEMIC STAFF

Students are encouraged to contact directly any member of staff whose lectures they haveattended if further help or advice is needed. Staff can also be contacted through the MACSOffice (EM1.25).

The academic staff for 2012-13 are listed below, together with their offices and telephoneextensions (prefix by 451 if calling from outside). E-mail addresses for staff consist of theinitials and surname followed by @hw.ac.uk (e.g. [email protected]).

Professor A.J.G. Cairns . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .CM S.08 3245

Dr R. Cruise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .CMT.27 3741

Dr C. Donnelly . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . CMG.04 3251

Professor S. Foss . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .CMG.07 3238

Professor G.J. Gibson (1st yr Director of Studies) . . . . . . . CM F.07 3205

Dr J. Hansen (4th yr Director of Studies) . . . . . . . . . . . . . . . CMT.22 3213

Dr T.C. Johnson . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .CMG.05 8343

Dr T. Kleinow (3rd yr Director of Studies) . . . . . . . . . . . . . . CM F.11 3252

Professor A.S. Macdonald (Head of AMS) . . . . . . . . . . . . . . .CMT.04 3209

Professor A. J. McNeil . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . CM S.05 3230

Mr J. Phillips (2nd yr Director of Studies) . . . . . . . . . . . . . . .CM S.06 4376

Mr P. Ridges (Exemptions Officer) . . . . . . . . . . . . . . . . . . . . . .CM F.13 3906

Mr G.G. Reid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .CM F.09 3075

Ms A.E. Sneddon . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . CM S.10 3226

Mr A.D. Stott . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . CM S.19 8293

Dr G. Streftaris . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .CM S.15 3679

Dr V. Shneer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . CMT.17 3902

Professor H.R. Waters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . CMT.06 3211

Dr A. Wiese . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . CMT.13 3717

Dr F. Yuen . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . CMG.20 8158

6

UNIVERSITY PRIZES & BURSARIES

A number of prizes, for overall performance in each year, are available to AMS students.

Year 1 Year 2University Prize University PrizeStandard Life Prize (may be shared) Worshipful Company of Actuaries Prize

(may be shared)

Year 3 Year 4University Prize Watt Club Medal for the best studentScottish Widows Prize (may be shared) IMA PrizeLongevitas Prize for Survival Models Roger Gray Memorial Prize in Statistics

The Company of Actuaries Charitable Trust offers a number of bursaries each year to finalyear honours students in Actuarial Science. Applicants are required to demonstrate needand reasonable progress on their degree, and should be seriously considering a career in theactuarial profession. Third year students who wish to apply should contact Dr J. Hansenat the beginning of the 2nd semester.

EXCHANGE OPPORTUNITIES

There are two exchange agreements which give AMS students the opportunity to studyabroad, at either the University of Melbourne (Australia) or the University of Waterloo(Canada). To be eligible, students will have to be consistently in the top fifth of theclass. For further information, see www.ma.hw.ac.uk/ams/teach/exchanges. Note thatthe Institute and Faculty of Actuaries accreditation policy does not apply to exchangeprogrammes; exemptions will be determined on a subject-by-subject basis (see p16).

INDUSTRIAL PLACEMENTS

The department allows students to undertake a twelve month actuarial placement betweenthe 2nd and 3rd, or 3rd and 4th years of their degree. The University’s Careers AdvisoryService and the AMS careers advisor, Mr G. Reid, can advise anyone interested on how togo about researching and applying for an internship.

7

COURSE & EXAMINATION REQUIREMENTS

Attendance

In order to satisfy course requirements, a satisfactory record of attendance at lectures andtutorials is required. Coursework must be handed in by the stipulated dates, and studentsare required to see their personal mentors at agreed times.

All lectures and tutorials are compulsory and registers of attendance will be taken inmost classes. Students who fail to satisfy the attendance requirements, or fail to submitcompulsory coursework for any of the courses for which they are registered may, after duewarning, be disallowed from presenting themselves for examination in those courses. (Fordetails, see www.hw.ac.uk/registry/.)

If you are absent from class due to illness for four days or less, you should complete aself-certification form, obtainable from the MACS office (EM1.25), and return it therewithin a week of your return. If you are absent for more than four days, you must supplya Special Circumstances Form (see p5) to the MACS office within a week of your return.

Examinations

It is the student’s responsibility to check all relevant examination timetables (includingresits) on the Registry web page www.hw.ac.uk/registry/. Should you be required toresit any exams, you must be available to take them. Therefore, do not book holidaysor take on any other commitments during the resit diet. (Note, you can apply totake resits at an overseas centre.)

Any basic scientific calculator other than graphics calculators, programmable calculators,or those with text storage or retrievable facilities may be used in examinations. (Cal-culators are not provided.) Students are not allowed to have mobile phones or othercommunication devices on or about their person during examinations. Phones may be leftat the front of the examination room but must be switched off.

Changes to Registration

Students should make any changes to course or degree registration through the relevantDirector of Studies (see p6). Any changes must be made before the end of week 3 of theterm, or a fine will be incurred. Forms can be obtained from the MACS Office (EM1.25)or www.hw.ac.uk/registry/resourses/changeofcourseform.pdf.

PLAGIARISM & CHEATING

Cheating in examinations and plagiarism, that is, the presentation of another person’sideas or work as one’s own, are very serious offences and are dealt with severely. Theycarry a range of penalties up to and including expulsion from the University. Studentsare responsible for familiarising themselves with University policy on these matters. Formore detail, see the MACS Guide, and the sections on Plagiarism and Regulation 9 at theRegistry’s website.

8

COURSE INFORMATION

Course Structure & Assessment

The academic year is divided into two semesters. Each semester consists of 12 weeksteaching followed by an assessment period (2 weeks in Semester 1, and 4 weeks in Semester2, following the Easter break). Students must register for 4 courses each semester, someof which are mandatory and others which are optional. These courses are listed in therelevant tables overleaf. Each course has a six-character code; the first two charactersindicate the department, the third is the level (0, 1 indicate Levels 10, 11 respectively),and the sixth is the term in which it is taught. Usually, but not always, Level 7 coursesare taken in the 1st year, and Level 8, 9 and 10/11 courses in the 2nd, 3rd and 4th yearsrespectively. A course is regarded as requiring 150 hours of student effort, and is worth 15SCQF credits.

Assessment

Each course is awarded a grade in the range A-F: grade E is the minimum requiredfor the award of credits, but at least a grade D is needed for progression to subsequentcourses. Other grades are interpreted as follows: A - excellent, B - very good, C - good,F - inadequate. (See University Regulations for further details.)The minimum mark needed to gain a grade D is usually 40%. The correspondence betweenmarks and other grades varies from course to course, but is approximately as follows: gradeA, 70% or over; grade B, 60-69%; grade C, 50-59%; grade D, 40-49%.

Level 7 & 8 CoursesCourse assessment is generally based on either coursework, an exam at the end of thesemester, or a combination of both. Details for individual courses can be found in therelevant course description (pp.19-23). If you do not obtain a grade D (or higher) in aLevel 7 or 8 course at the first attempt, you are entitled to one further attempt.

Level 9, 10 & 11 CoursesAssessment of Level 9, 10 and 11 courses is generally as for Level 7 and 8. However, insome cases, the exam for a first semester course may take place at the end of the secondsemester. Also, note that some pairs of courses are synoptically linked; that is, both coursesare assigned the same grade, based on the average mark for the individual courses. Detailsare in the relevant course description (pp.24-35). All Level 9, 10 and 11 course markscount towards the final degree classification (see also Proceeding to the 4th year, p13).

Results and Progress Decisions

The Progression Board meets at the end of the academic year to decide which students willbe allowed to proceed to the next year of their degree programme. The Director of Studieswill write to inform you of the Board’s decision, and whether you must resit any exams.The Registry also makes the results available online. Final year students receive a letterfrom the Registry containing a complete list of their results and confirmation of degreeclassification. To avoid any delay in receiving your letter, you should inform the MACSoffice (EM1.25) of your summer address if it will not be the same as your permanent homeaddress.

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First Year Courses

1st Semester Courses Req’d Opt.

F77SA1 Introduction to Statistical Science A AS, FM, SM

F17CA1 Calculus A AS, FM, SM

F17CC1 Algebra A AS, FM, SM

C27OA1 Introductory Economics FM AS, SM

2nd Semester Courses Req’d Opt.

F77SB2 Introduction to Statistical Science B AS, FM, SM

F17CB2 Calculus B AS, FM, SM

F77PD2 Professional Development Planning AS, FM, SM

C37FF2 Finance & Financial Reporting FM AS, SM

AS − Actuarial Science FM − Financial Mathematics SM − Statistical Modelling

Degree Requirements:

Actuarial Science and Statistical ModellingThree mandatory and one optional course1 each semester.AS students should note that the options C37FF2 and C27OA1 can lead to exemptionsfrom the CT2 and CT7 examinations of the Institute and Faculty of Actuaries (see Ac-tuarial Exemptions, p16).

Financial MathematicsEight mandatory courses.

Proceeding to 2nd Year

If you obtain a grade D or better in all 8 courses at the first attempt , you may proceed tothe 2nd year of any AMS degree for which you have fulfilled the prerequisites.

Otherwise, progress is determined by the progression board on a case-by-case basis, andyou may be required to resit some exams in August. If you do not obtain D’s at thisattempt, you may be required to transfer to another degree programme for which youhave enough credit points (e.g. Combined Studies, Mathematics), or withdraw from theUniversity. You will be advised of your options.

1 Any Level 7 course may be chosen as an option, subject to timetable constraints andthe approval of the Director of Studies.

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Second Year Courses


F78PA1 Probability & Statistics A AS, FM, SM

F78AA1 Actuarial & Financial Mathematics A AS, FM, SM

F18CD1 Multivariable Calculus & Real Analysis A AS, FM, SM

F18CF1 Linear Algebra AS, FM, SM


F78PB2 Probability & Statistics B AS, FM, SM

F78AB2 Actuarial & Financial Mathematics B AS, FM, SM

F18CE2 Multivariable Calculus & Real Analysis B AS, FM, SM

F18NA2 Numerical Analysis A AS, FM, SM

C37FF2 Finance & Financial Reporting AS, FM, SM



Actuarial Science, Financial Mathematics and Statistical ModellingSeven mandatory courses, plus one optional course1,2 in Semester 2.AS students should note that C37FF2 can lead to exemption from the CT2 examinationof the Institute and Faculty of Actuaries (see Actuarial Exemptions, p16).

Proceeding to 3rd Year

If you obtain a grade D or better in all 8 courses at the first attempt , you may be allowedto proceed to the 3rd year of any AMS degree for which you have fulfilled the prerequisites.

Otherwise, progress is determined by the progression board on a case-by-case basis, andyou may be required to resit some exams in August. If you do not obtain D’s at thisattempt, you may be required to transfer to another degree programme for which youhave enough credit points (e.g. Combined Studies, Mathematics), or withdraw from theUniversity. You will be advised of your options.

1 SM students may chose any Level 7 or 8 course as an option, subject to timetableconstraints and the approval of the Director of Studies.

2 Direct entrant FM students must take C37FF2 to fulfil degree requirements.

11

Third Year Courses


F79MA1 Statistical Models A AS, FM, SM

F79SP1 Stochastic Processes AS, FM, SM

F79PS1 Statistics for Social Science SM

F70LA1 Life Insurance Mathematics A AS

F79PA1 Portfolio Theory & Asset Models AS, FM SM

C27OA1 Introductory Economics FM

F19MV1 Vector Analysis FM, SM


F79MB2 Statistical Models B AS, FM, SM

F79BI2 Bayesian Inference & Computational Methods SM FM

F79SU2 Survival Models AS, SM

F70LB2 Life Insurance Mathematics B AS

F79DF2 Derivative Markets & Discrete-time Finance AS, FM SM

F19MO2 Ordinary Differential Equations FM SM

F19NB2 Numerical Analysis B FM


12


Actuarial ScienceEight mandatory courses.

Financial MathematicsThree mandatory and one optional course1 each semester.

Statistical ModellingThree mandatory and one optional course2 each semester.

Synoptic Links (see p9)

The following pairs of courses are synoptically linked:F79MA1 and F79MB2,F79SP1 and F79SU2 (not FM degree),F79PA1 and F79DF2 (not SM degree),F70LA1 and F70LB2.

Proceeding to 4th Year

If you obtain a grade D or better in all 8 courses, the examiners may allow you to proceedto the 4th year. If you obtain a grade D or better in at least 6 courses and have anaverage mark of at least 40%, you may be permitted, at the discretion of the examiners ,to proceed to the 4th year of an AMS degree. In these cases you will be advised by theexaminers of your options, and may be required to resit some papers in August, to satisfythe prerequisites for the 4th year courses. However, note that otherwise, no resit is allowedfor an Honours paper, and in all cases, it is the marks obtained at the first attempt thatform part of the final degree assessment (see p15). For further information, consult yourmentor.

Ordinary Degrees

A candidate who obtains a grade D or better in at least four Level 9 courses and a totalof at least 360 credits may be awarded the ordinary degree of B.Sc.

1 Direct entrant FM students must take C27OA1 to fulfil degree requirements.2 SM students may chose any Level 7, 8 or 9 course as an option, subject to timetable

constraints and the approval of the Director of Studies. However, note that only 9th- and10th-level courses count towards the final degree assessment (see Final Degree Assess-ment, p15).

13

Fourth Year Courses

1st Semester Courses Req’d Opt. Elect.

F70DA1 Statistics Dissertation A SM

F79PS1 Statistics for Social Science AS, FM

F70SC1 Statistical Computing SM

F70CF1 Continuous-time Finance FM AS, SM

F71RM1 Financial Risk Management FM, AS, SM

F70PE1 Pensions AS

F10MF1 Functional Analysis FM

F10MM1 Optimisation SM AS, FM

F19MV1 Vector Analysis AS

F10AM1 Mathematical Biology A SM

F10NC1 Numerical Analysis C FM, SM

C39SM1 International Bond and Currency Markets FM AS



Actuarial ScienceAt least 3 optional courses1 plus at most 1 elective course2 each semester.Note: AS students must take both F70PE1 and F70LP2, or neither.

Financial MathematicsOne mandatory course and three optional courses each semester. At least four optioncourses must be at Level 10 or above.

Statistical ModellingTwo mandatory courses plus at least one optional course and at most one elective eachsemester.Note: students transferring to the SM degree from one of the other AMS degrees musttake F79PS1 and F79BI2 (if not already taken).

1 Direct entrants to 3rd year AS may take F71AB1 to obtain exemption from the CT1examination of the Institute and Faculty of Actuaries.

2 Direct entrants to AS may take C27OA1 and/or C37FF2 to obtain exemption fromthe CT7 and/or CT2 examinations of the Institute and Faculty of Actuaries.

14

2nd Semester Courses Req’d Opt. Elect.

F70DB2 Statistics Dissertation B SM

F70ST2 Statistics Special Topic SM

F70TS2 Time Series SM AS, FM

F79BI2 Bayesian Inference & Computational Methods AS, FM

F70DP2 Advanced Derivative Pricing FM

F70RT2 Risk Theory AS, FM, SM

F70LP2 Life Office Practice AS

F71CM2 Credit Risk Modelling FM

F19MO2 Ordinary Differential Equations AS

F10AN2 Mathematical Biology B SM

F10ND2 Numerical Analysis D FM, SM

C39TA2 Taxation (Tax Law) AS

Synoptic Links (see p9)

The following pairs of courses are synoptically linked:F70DA1 and F70DB2,F70PE1 and F70LP2.

Final Degree Assessment

The Examiners take into account all Level 9 and above course marks in deciding the classof Honours: the final mark is the average of those marks (note that 7th- and 8th-levelcourse marks are not included). In broad terms, an average mark of over 70% for firstclass honours, 60% - 70% for upper second class honours, 50% - 60% for lower secondclass honours, and 40% - 50% for third class honours, would be required, subject to theagreement of the Examiners. (Note that 480 credits are required for the award of anhonours degree.) To ensure that students offering more Level 9 or above courses are notat a disadvantage relative to those offering fewer, the Examiners will take steps to ensurecomparability of treatment and class of degree awarded. In borderline cases, a positiveview is taken of an improving performance from third to fourth year.

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ACTUARIAL EXEMPTIONS

The Actuarial Science degree has been accredited by the UK Actuarial Profession, whichmeans that students can obtain exemption from some of the subjects in the Institute andFaculty of Actuaries’ examination system. There are two routes to gaining exemptions.

Students graduating with a good upper second class degree (normally an overall averageof at least 65%) will be eligible for exemption from all the Core Technical Subjects CT1-8covered in their degree in which they have attained the University pass mark (normally40%).

Students who do not attain the accreditation threshold as above will be considered forexemption from individual subjects as described below. The exemption standard for eachsubject will be reviewed each year by the profession’s Independent Examiners and mayvary from year to year.

Note that the accreditation policy does not cover exchange arrangements; all exemptionswill be recommended on a subject-by-subject basis, taking into account performance atHeriot-Watt and the exchange university.

Further information can be found at the profession’s website (www.actuaries.org.uk/).

Core Technical Stage

Exemptions are based on performance in the relevant subjects as listed below.

Subject CT1 Financial Mathematics:

Actuarial & Financial Mathematics F78AA1, F78AB2.

Subject CT2 Finance & Financial Reporting:

Finance & Financial Reporting C37FF2.

Subject CT3 Probability & Mathematical Statistics:

Probability & Statistics F78PA1, F78PB2.

Subject CT4 Models:

Survival Models F79SP1, Stochastic Processes F79SU2.

Subject CT5 Contingencies:

Life Insurance Mathematics F70LA1, F70LB2.

Subject CT6 Statistical Methods:

Risk Theory F70RT2, Time Series F70TS2.

Subject CT7 Economics:

Introductory Economics C27OA1.

Subject CT8 Financial Economics:

Portfolio Th. F79PA1, Derivative Markets F79DF2, Continuous-time Finance F70CF1.

Subject CT9 Business Awareness:

The profession assesses this through a two-day residential course. There are no exemptions.

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Later Stages of the Professional Syllabus

The later parts of the professional syllabus are divided into three stages: Core Applications,Specialist Technical, and Specialist Applications. In addition, the profession intends todevelop a series of UK Practice Modules, which will not be required to qualify as a Fellow,but will be required in order to practise in the UK. Students on the M.Sc. in ActuarialManagement can obtain exemptions from CA1, CA3 and two ST subjects. Otherwise, noexemptions are available, although some courses are relevant, as indicated in the brackets.

Core Applications Stage

Subject CA1 Core Applications Concepts

Subject CA2 Modelling Module

Subject CA3 Communications

Specialist Technical Stage (students choose two subjects)(Note Subject ST3 no longer exists.)

Subject ST1 Health and Care

Subject ST2 Life Insurance (F70LP2)

Subject ST4 Pensions and Other Benefits (F70PE1)

Subject ST5 Finance and Investment A

Subject ST6 Finance and Investment B (F70CF1, F79DF2)

Subject ST7 General Insurance: Reserving and Capital Modelling (F70RT2)

Subject ST8 General Insurance: Pricing (F70RT2)

Subject ST9 Enterprise Risk Management (F71RM1)

Specialist Applications Stage (students choose one subject)

Subject SA1 Health and Care

Subject SA2 Life Insurance (F70LP2)

Subject SA3 General Insurance

Subject SA4 Pensions and Employee Benefits (F70PE1)

Subject SA5 Finance

Subject SA6 Investment

It is also possible to pass the Specialist Applications stage by writing a research dissertation(Subject SA0).

Some general points to note about the exemption system are:

1. The University cannot grant exemptions, it can only recommend them to the Instituteand Faculty of Actuaries. Usually, the recommendations are accepted.

2. Decisions regarding recommendations for exemptions are generally made on the basisof the student’s performance at the first sitting of the relevant University exam. (Resitsgranted as a first attempt because of medical or other special circumstances are usually

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counted as a first attempt for exemption purposes also.) From the academic year 2012–13, the Institute and Faculty of Actuaries will only allow a student to resit a coursefor exemption purposes (in the absence of special circumstances) if it is necessary toresit it for the purposes of progression or graduation, in which case the resit mustbe taken at the next reassessment opportunity, and the maximum mark that can beused for exemption purposes is the pass mark (40%). These resits are for subject-by-subject exemptions only, and will not alter your degree average, or your entitlementto exemptions from other courses under the accreditation agreement.

Note that this is a change from previous years in the Institute and Faculty’s policy.

3. Decisions on a particular exemption are made at a meeting of staff and an independentexaminer held at the end of the academic year in which the relevant informationbecomes available, following which students are informed of these decisions. However,the recommendations are not sent to the Institute and Faculty until the end of theacademic year in which the student graduates. Graduating students will be issuedwith a letter confirming the recommendations, and advising on how to claim themupon joining the Institute and Faculty of Actuaries as a student member.

4. The Institute and Faculty of Actuaries will not grant any exemptions (or confirmthat any will be granted) until a student has joined the profession, at which time youshould complete an Exemptions Application Form, available from the Institute andFaculty. State clearly on the form that you are a graduate of the AMS Departmentat Heriot-Watt University; there will then be no need to supply details of syllabi orexam papers. Note there is a fee payable for each exemption granted.

5. There are frequent discussions between the AMS department and the profession aboutthe rules and practices concerning exemptions. The above notes reflect the currentposition but it is possible that changes may occur without prior notice.

6. Any further questions can be addressed to Mr P. Ridges.

MISCELLANEOUS

Lockers

Lockers are allocated for the duration of each academic year on a first-come, first-servedbasis. Keys for lockers in the EM Building are available from Mr A. Houston (EM1.31)for a deposit of -L10.Mail & Notices

Mail (internal and external) for students is delivered to pigeon-holes outside the MACSOffice (EM1.25). Check yours regularly. Various notices are posted on the noticeboardoutside CMS.01, including copies of the timetables.

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AMS COURSE DESCRIPTIONS (2012-13)

Information about courses in the Mathematics Department and the School of Management& Languages can be found at the relevant web sites:

http://www.ma.hw.ac.uk/maths/courseinfo/index.phphttp://www.sml.hw.ac.uk/undergraduate/course/index.html.

Level 7 Courses

F77SA1 INTRODUCTION TOSTATISTICAL SCIENCE A

Lecturer: J. Hansen

Aims: To provide an introduction to the statistical issues associated with the collec-tion, description, and interpretation of data, and in addition, to introduce computer-basedmethods for graphically describing and summarising data.

Summary: The aim of statistical analysis is to provide insight by means of numbers.This process usually involves three stages:1. collecting data,2. describing and presenting data,3. drawing conclusions from the data (inference).

In this course, we will (primarily) consider the statistical principles and techniques usedin the first two stages in an analysis. There will be some discussion of inference at the endof the course.

Book:D.S. Moore and W. Notz, Statistics: Concepts and Controversies 6th ed. (W.H.Freeman & Co.).

Assessment: Continuous assessment: two 1-hour class tests (35% each) and a data anal-ysis project (30%).

F77SB2 INTRODUCTION TOSTATISTICAL SCIENCE B

Lecturer: J. Hansen

Aims: To develop simple probability models for data and understand important featuresof these models.

Summary: This course provides an introduction to the probability models for inference.The main topics covered are:1. models for statistical inference: introduction to discrete probability models including

sample spaces, probability functions, axioms of probability and consequences of theaxioms;

2. conditional probability, Partition Theorem, Bayes’ Theorem and independence;3. special probability models for random experiments;4. discrete random variables, expectation and variance.

Book: (useful, but not essential)S. M. Ross, A First Course in Probability, 7th ed. (Pearson, 2006).

Assessment: 2 hour final exam (80%), 2 marked assignments (10% each).

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F77PD2 PROFESSIONAL DEVELOPMENTPLANNING

Lecturers: Various

Aims: To introduce students to the actuarial, statistical and financial mathematics pro-fessions and to improve their career planning. To help students build up a range of skillsthat will prepare them to cope well at the job interview stage and beyond.

Summary:1. An analysis of the opportunities available to Actuarial Science, Financial Mathematics

and Statistical Modelling graduates;2. Case studies of career paths taken by graduates in these subject areas;3. Professional Development Planning and the graduate selection process;4. Using computer methods to solve problems of the type found in industry;5. Taking part in games that simulate the business environment.

Assessment: Continuous assessment: group project analysing a particular company, pre-sentation, written assignments and two computer projects.

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Level 8 Courses

F78PA1 PROBABILITY & STATISTICS A Lecturer: J. Hansen

Aims: To develop the tools of probability theory with a view to applications in statisticalinference and actuarial science, and to provide an introduction to computer simulation andits applications to probability and statistics

Summary: The main topics covered in this course are:1. Probability models: sample spaces, events, probability measures, axioms of probability

and related results.2. Random variables and their distributions.3. Expectation, variance, and standard deviation of random variables.4. Important random variables including Binomial, Geometric, Hypergeometric, Poisson,

Uniform, Normal, Lognormal, Exponential, Gamma variables.5. Conditional probability and independence including the chain rule, the partition rule

and Bayes’ Theorem.6. Joint probability distributions, marginal and conditional distributions.7. Independent random variables and sums of independent random variables, generating

functions, the weak law of large numbers and the Central Limit Theorem.8. Expectation of a function of random variables, covariance and correlation.9. Computer simulation of random variables and its applications in probability and statis-

tics.

Prerequisites: F77SA and F77SB (or equivalent).

Books: Some helpful reference books include:G. Grimmett & D. Welsh, Probability: An Introduction (Oxford Science, 1990);S.M. Ross, A First Course in Probability, 7th ed. (Pearson, 2006);D. Stirzaker, Probability and Random Variables: a beginner’s guide (CUP, 1999).

Assessment: 2 hour end-of-semester examination (85%), continuous assessment(15%).

F78PB2 PROBABILITY & STATISTICS B Lecturer: J. Phillips

Aims: To reinforce basic ideas related to the description and analysis of data, and providethe basis for the application of statistical modelling, estimation, hypothesis testing andregression.

Summary: This course follows on from Probability and Statistics A. It develops the basicideas used in statistical analysis and inference, with an emphasis on how we learn fromdata using both graphical techniques and statistical methodology based on probability the-ory. Topics presented include: analysis of simple data; construction of statistical models;sampling distributions and properties of estimators; method of moments and introductionto maximum likelihood estimation; inference for data from one population; comparisons ofdata from two populations; confidence intervals with samples from one or two populations;hypothesis testing; issues related to association between two variables; linear regression;statistical computing.

Prerequisites: F77SA1 and F77SB2 (or equivalent).

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Books:I. Miller & M. Miller, J. E. Freund’s Mathematical Statistics with Applications, 7thed. (Prentice Hall, 2004).

Assessment: 2 hour end-of-semester examination (80%), continuous assessment (20%).

F78AA1 ACTUARIAL & FINANCIALMATHEMATICS A

Lecturer: A.S. Macdonald

Aims: The aim of this course, along with F78AB2, is to give students a thorough un-derstanding of basic actuarial techniques. Exemptions from Subject CT1 may be recom-mended for candidates who score sufficiently well in F78AA1 and F78AB2. (see ActuarialExemptions, p16.)

Summary: In this course, you will learn how to deal with questions involving cash-flowsat discrete time points, and the accumulation and discounting of payments over discretetime intervals. Topics include:1. interest rates and some actuarial notation;2. loan schedules;3. yields;4. fixed interest securities;5. inflation indexing;6. discounted cash flows.

There are three lectures per week. Students attend one tutorial or computer laboratoryper week.

Books: Useful reference:J. J. McCutcheon & W.F. Scott, An Introduction to the Mathematics of Finance.

Details on obtaining this book will be distributed by the lecturer. Alternative referencewith additional exercises:

Schaum’s Outlines of Mathematics of Finance (McGraw-Hill, 1996).

Assessment: 2 hour end-of-semester examination (90%), Excel-based assignment (10%).

F78AB2 ACTUARIAL & FINANCIALMATHEMATICS B

Lecturer: C. Donnelly

Aims:1. To introduce the continuous-time concept of cashflows and interest,2. develop skills in applying continuous-time models to financial contracts and transac-

tions,3. model interest rates as random variables and apply those models,4. introduce the principle of no-arbitrage and how to price financial contracts and con-

struct the term-structure of interest rates assuming no-arbitrage,5. introduce simple survival models and life tables.

Summary: This course builds on and extends the ideas contained in the related courseF78AA1. The concepts of a continuously-payable cashflow and the force of interest areconsidered. We see how interest-rate risk can be managed through the use of Redington’s

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immunisation theory. As rates of return can be random, we see how to model them usingrandom variables. Using the no-arbitrage principle, we price forward contracts. This leadson to a wider discussion of the term-structure of interest rates and the yield curve.

Life insurance is one of the core areas of actuarial science. We introduce survival modelsand life tables, and see how to model the future lifetime of an individual as a randomvariable. The course examines some of the functions associated with survival models,which are essential knowledge required for the 3rd year courses in survival models and lifeinsurance mathematics.

Books:D.C.M. Dickson, M.R. Hardy & H.R. Waters, Actuarial Mathematics for Life Con-tingent Risks (Cambridge University Press, 2009);J. C. Hull, Options, Futures and Other Derivatives (Prentice Hall);J.J. McCutcheon & W.F. Scott, An Introduction to the Mathematics of Finance (pub-lished for the Institute and Faculty of Actuaries, 1995).

Assessment: As for F78AA1.

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Level 9 Courses

Students on the Actuarial Science degree, see F70LA1, F70LB2 on p30.

F79MA1 STATISTICAL MODELS A Lecturer: G.J. Gibson

Aims: To describe and compare the main approaches to statistical inference, includingclassical and Bayesian, and to develop students’ skills in practical, computer-based estima-tion and inference. This course also aims to develop students’ independent research skills,and their report writing skills.

Summary: This course will consist of a mixture of lectures, tutorials, and project work.First and second year courses have discussed how to draw conclusions from data, and intro-duced some basic methods in an informal way. In this course we take a more fundamentalapproach to estimation and quantifying the accuracy of estimates.In lectures we introduce the principles of classical and Bayesian inference discussing theirdifferent philosophical bases, and comparing the different solutions that each method givesto various problems of inference. The properties and fundamental importance of the like-lihood are described, along with some important results on the sampling properties ofestimators.The course will emphasise worked examples and there will be project work based on thecomputer implementation of the theory taught in lectures and tutorials. The statisticalcomputer package R will be used for the project work.

Prerequisites: F78PA1 and F78PB2 (or equivalent).

Books:(useful) P.H. Garthwaite et al, Statistical Inference, 2nd ed. (Oxford Science Publ.,2002);G. Casella & R.L. Berger, Statistical Inference (Duxbury Press, 1990);(background) V. Barnett, Comparative Statistical Inference, 3rd ed. (Wiley, 1999).

Assessment: 2 hour exam on the lecture material in December (60%) and a project(40%). This course is synoptically linked with F79MB2.

F79MB2 STATISTICAL MODELS B Lecturer: G. Streftaris

Aims: To develop students abilities in understanding and solving statistical problems,and to teach them how to choose appropriate techniques, analyse data and present results,especially in applications related to linear and generalised linear models.

Summary: The course will consist of a mixture of lectures and practical work. Thefirst part of the course will focus on statistical modelling, including the selection of ap-propriate models, the analysis and interpretation of results, and diagnostics. Exploratoryand graphical techniques will be considered, as well as more formal statistical procedures.Both parametric and nonparametric methods will be discussed, as will modern robusttechniques. There will be considerable emphasis on examples, applications and case stud-ies, especially for continuous response variables. Some theory of multiple linear regressionin matrix notation will be presented. The course will go on to consider the theory and

24

techniques for the analysis of categorical data, including the use of generalised linear mod-els (log-linear and logistic regression models). Practical applications will be emphasisedthroughout and computing facilities, especially R, will be used extensively.


Books: The following textbooks are recommended:

A.J. Dobson, An Introduction to Generalized Linear Models, 2nd ed. (Chapman &Hall, 2002) (reference);

J. Faraway, Linear models with R (Chapman & Hall, 2005);

J. Faraway Extending the Linear Model with R: Generalized Linear, Mixed Effects andNonparametric Regression Models (Chapman & Hall/CRC, 2006);

P.H. Garthwaite, I.T. Jolliffe & B. Jones, Statistical Inference, 2nd ed. (Prentice Hall,2002);

J. Verzani, Using R for Introductory Statistics (Chapman & Hall/CRC, 2005) (back-ground);

S. Weisberg, Applied linear regression, 3rd ed. (Wiley/Interscience, 2005).

Assessment: Two practical assignments, to be handed in at specified times during thesemester. This course is synoptically linked with F79MA1.

F79PS1 STATISTICS FOR SOCIAL SCIENCE Lecturer: J. Phillips

Aims: To introduce students to the main classical statistical methods that are commonlyapplied in psychology and other social sciences and to give hands-on experience of usingmore advanced techniques for exploring multivariate data.

Summary: In social sciences, such as psychology, experiments and surveys typically yieldlarge quantities of high-dimensional data (e.g. in the form of questionnaire responses)from which we wish to extract simpler underlying relationships, or evidence of differencesin subgroups in a population. The course will give students a grounding in the mostcommon classical statistical methods used in analysing psychological data, the correct in-terpretation of results, and the application of methods to real data sets using the computerpackage SPSS. Topics covered will include: confidence intervals, hypotheses testing, para-metric and nonparametric statistical methods, analysis of variance (incorporating one-waydesigns, planned and unplanned comparisons, factorial designs and interactions), principalcomponents analysis and the interpretation and use of factor analysis.

Prerequisites: F78PA1 and F78PB2, or F78SC2 (or equivalent).

Books:

Brace, Kemp & Snelgar, SPSS for Psychologists, 3rd ed. (Palgrave Macmillan, 2006);

H. Coolican, Research Methods and Statistics in Psychology (Hodder & Stoughton,1999);

D.C. Howell, Statistical Methods for Psychology , 5th ed. (Duxbury, 2002).

Assessment: 2 hour exam in December (60%) and project work (40%).

25

F79SP1 STOCHASTIC PROCESSES Lecturer: S. Foss

Aims: To introduce fundamental stochastic processes which are useful in insurance, in-vestment and stochastic modelling, and to develop techniques and methods for analysingthe long term behaviour of these processes.

Summary: In this course, we develop methods for modelling systems or quantities whichchange randomly with time. Specifically, the evolution of a system is described by acollection {Xt} of random variables, where Xt denotes the state of the system at time t.

Discrete-time processes studied include Markov chains. In particular, we consider branch-ing processes, random walk processes, and more general countable state-space chains.

Continuous-time processes studied include point processes, Poisson and compound Poissonprocesses; continuous time Markov processes; population, queueing and risk models.


Books: Useful reference books areP. Bremaud, An Introduction to Probabilistic Modeling, (Springer, 1997);Grimmett & Stirzaker, Probability and Random Processes, 3rd ed. (OUP, 2001);Grinstead & Snell, Introduction to Probability, (Amer. Math. Soc., 1997);W. Feller, An Introduction to Probability Theory and Its Applications, Vol. 1, 3rd ed.(Wiley, 1968);S.M. Ross, Stochastic Processes, 2nd ed. (Wiley, 1996).

Assessment: 2 hour exam at the end of the 1st semester. This course is synopticallylinked to F79SU2 on all degrees except FM.

F79BI2 BAYESIAN INFERENCE &COMPUTATIONAL METHODS

Lecturer: G.J. Gibson

Aims: To provide students with a knowledge of modern Bayesian statistical inference, anunderstanding of the theory and application of stochastic simulation methods includingMCMC, and experience of implementing the Bayesian approach in practical situations.

Summary: The course will review subjective and frequentist probability, the role oflikelihood as a basis for inference, and give a comparative treatment of Bayesian andfrequentist approaches. The key concepts in practical Bayesian statistics will be coveredincluding: likelihood formulation; the incorporation of prior knowledge or ignorance in theprior; the interpretation of the posterior distribution as the totality of knowledge and itsuse in prediction. A range of stochastic simulation methods for investigating posteriordistributions will be considered. Methods will include rejection sampling, and Markovchain methods such as the Metropolis-Hastings algorithm and the Gibbs sampler. The useof stochastic methods for inference for partially observed processes will be discussed andstudents will gain experience of implementing methods in computer laboratory sessions.


Books:(useful) P.H. Garthwaite et al, Statistical Inference, 2nd ed. (Oxford Sc. Publ., 2002);W.M Bolstad, Introduction to Bayesian Statistics (Wiley, 2004).

Assessment: 2 hour exam (60%) and 2 practical assignments (20% each).

26

F79PA1 PORTFOLIO THEORY & ASSET MODELS Lecturer: F. Yuen

Aims: To introduce asset pricing and portfolio selection models. This course coversthe first half of the material in Subject CT8 of the Institute and Faculty of Actuariesexaminations.

Summary: This course covers the following topics: utility theory, stochastic dominance,measures of investment risk, portfolio theory, models of asset returns, equilibrium models,and efficient markets hypothesis.

Prerequisites: F78PA1 and F78AB2 (or equivalent).

Books:(Main reference) Brown, Elton, Goetzman & Gruber, Modern Portfolio Theory andInvestment Analysis , 8th ed. (Wiley, older editions are adequate);Boyle, Cox, Dufresne, Gerber, Mueller, Panjer, Pedersen, Pliska, Sherris, Shiu & Tan,Financial Economics (The Actuarial Foundation, Chicago, 1998).

Assessment: 2 hour exam at the end of the 1st semester. This course is synopticallylinked to F79DF2 on all degrees except SM.

F79DF2 DERIVATIVE MARKETS &DISCRETE-TIME FINANCE

Lecturer: T.C. Johnson

Aims: This course introduces students to derivatives, their use in financial markets andhow they are priced and hedged in discrete time. It introduces the relationship betweenfinancial markets and stochastic analysis.

Summary: The course introduces the idea of derivative securities and why they exist,explaining the role of forward and option contracts in risk management, and discussesvarious investment strategies involving derivatives. The concept of arbitrage-free pricing(cash-and-carry pricing) is explained and developed into the fundamental theorem of assetpricing in discrete time. Pricing on the binomial tree (the CRR model) is explained,for both European- and American-style derivatives, in the context of the fundamentaltheorem, and the relationship between the CRR model and the continuous-time Black-Scholes-Merton formula is discussed. The fundamental properties of option prices aregiven.

This course covers some of the material in Subject CT8 of the Institute and Faculty ofActuaries examinations.

Prerequisites: F78PA1 and F78AB2 (or equivalent).

Books: Recommended texts areM. Baxter & A. Rennie, Financial Calculus (Cambridge University Press, 1996);M. Joshi, The Concepts and Practice of Mathematical Finance (CUP, 2003);S.R. Pliska, Introduction to Mathematical Finance (Blackwell, 2000);S. Shreve, Stochastic Calculus for Finance II: The Binomial Asset Pricing Model(Springer, 2004).

Assessment: 2 hour end-of-semester exam (80%), continuous assessment (20%). Thiscourse is synoptically linked to F79PA1 on all degrees except SM.

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F79SU2 SURVIVAL MODELS Lecturer: T. Kleinow

Aims:1. To understand the use of mathematical models of mortality, illness and other life-

history events in the study of processes of actuarial interest.2. To be able to estimate the parameters in these models, mainly by maximum likelihood.3. To describe and apply methods of smoothing rates of mortality and other other actu-

arial statistics based on observed data.

Summary:1. Estimation procedures for lifetime distributions: Kaplan-Meier estimate of the sur-

vival function, the Nelson-Aalen estimate of the cumulative hazard function and esti-mation for the Cox model for proportional hazards.

2. Statistical models for transfers between multiple states (e.g., alive, ill, dead), relation-ships between probabilities of transfer and transition intensities, and estimation forthe parameters in these models.

3. Tests of consistency of crude estimates of rates of mortality and rates in a standardtable. Methods of graduation: parametric, standard table, graphical.

4. Computing facilities, especially R, will be used extensively and this work will beassessed by practical assignments.

Prerequisites: F78AB2 and F78PB2 (or equivalent).

Book:I.D. Currie, Survival Models (Heriot-Watt University notes, supplied by the depart-ment).

Assessment: 2 hour exam (85%), project work (15%). This course is synoptically linkedto F79SP1 (except on the FM degree).

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Level 10/11 Courses

F70TS2 TIME SERIES Lecturer: P. Ridges

Aims: To introduce many of the fundamental concepts required for modelling and fore-casting time series data.

Summary: A time series is a set of data consisting of observations made one after anotherin time. The analysis of time series data is an area of practical importance in finance,business, economics, industry, medicine, life and physical sciences and many other fields.

The course begins with real data, and some descriptive methods for identifying, and re-moving if appropriate, trend and seasonal effects. We consider moving averages and expo-nential smoothing, along with other approaches. This leads into the important conceptsof stationarity and autocorrelation.

The main body of the course consists of modelling the stochastic mechanism which givesrise to an observed series, and then using model-based forecasting procedures to predictfuture values of the series. The models we consider are autoregressive moving average(ARMA) processes, and autoregressive integrated moving average (ARIMA) processes.Various methods of parameter estimation are considered, including the method of mo-ments, least-squares, conditional least-squares, and maximum likelihood. We then performresidual analysis, and consider over-fitting and the principle of parsimony. The course endswith consideration of various forecasting methods.

Although the approach is mainly orientated to utilising time-dependence, we also considerthe frequency aspects of series and study the periodogram and the spectral density. Werelate the two approaches.


Books: Useful references areC. Chatfield, The Analysis of Time Series (Chapman Hall);P. Diggle, Time Series (OUP);T.C. Mills, Time Series Techniques for Economists (CUP).

Assessment: 2 hour exam.

F70DA1F70DB2

STATISTICS DISSERTATION ASTATISTICS DISSERTATION B

Supervisors: R. CruiseG.J. GibsonG. Streftaris

Aims: To carry out an extensive study of a problem in probability or statistics, testingskills learnt from previous courses, and to develop skills in project work, including literaturesearch and the writing and presentation of reports.

Summary: Each student will do one project each semester. Students will be allocated tosupervisors on registration in October; precise topics and work plans will be decided bysupervisors in consultation with students.

Prerequisites: F79MA1 and F79MB2.

Assessment: 1 dissertation per course. These courses are synoptically linked.

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F70LA1 LIFE INSURANCE MATHEMATICS A Lecturer: P. Ridges

Aims: To extend the coverage of life assurance mathematics in F78AB2 to include someof the material for Subject CT5 of the Institute and Faculty of Actuaries examinations.

Summary: By combining the mathematics of finance and the mortality table, we candevelop the functions necessary to value a wide range of benefits which may be payableon death or survival. Some of the functions will be clear extensions of those previouslyencountered, while others will be new. Such benefits are often provided by insurancepolicies. The course will study some of the essential calculations made by insurance com-panies in valuing their contracts and calculating premiums. You will learn how to dealwith questions involving:

selection and select life tables,actuarial functions using select life tables,with profits policies,net premiums and gross premiums,expenses and bonuses,net and gross premium policy values.

There will be three lectures and one tutorial or computer lab per week.

Prerequisites: F78AA1 and F78AB2 (or equivalent).

Books:Formulae and Tables for Actuarial Examinations (several copies available in library).Dickson, Hardy & Waters, Actuarial Mathematics for Life Contingent Risks (CUP,2009). (F70LA1 covers material in the first seven chapters.)

Assessment: 2 hour exam (80%) at the end of the 1st semester and an Excel-basedassignment (20%). This course is synoptically linked with F70LB2.

F70LB2 LIFE INSURANCE MATHEMATICS B Lecturer: G.G. Reid

Aims: To extend the coverage of life assurance mathematics in F70LA1 to include furthermaterial for Subject CT5 of the Institute and Faculty of Actuaries examinations.

Summary: In this course, you will learn how to deal with questions involving:Thiele’s differential equation,Markov multiple-state models,risk reserves,insurances written on multiple lives,the features of disability and long-term care insurance contracts,heterogeneity and selection,single-figure indices,profit testing conventional insurance contracts,profit testing unit-linked contracts.

There will be three lectures and one tutorial or computer lab per week.

Prerequisites & books: See F70LA1.

Assessment: 2 hour exam (80%) at the end of the 2nd semester and an Excel-basedassignment (20%). This course is synoptically linked with F70LA1.

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F70CF1 CONTINUOUS-TIME FINANCE Lecturer: T. Kleinow

Aims: This course develops the theory and practice of financial derivatives pricing incontinuous time, following on from the course F79DF2 Derivatives Markets and Discrete-Time Finance.

Summary:1. Theory of martingales in continuous time, Brownian motion, and its properties, stochas-

tic integration, stochastic differential equations and Ito’s formula, Girsanov’s theoremand the Martingale Representation Theorem.

2. The Black-Scholes model, derivatives pricing using the martingale and PDE ap-proaches, extensions to foreign currencies and dividend-paying stocks.

3. Portfolio risk management.4. Interest rate models, and credit risk models.5. Other models of security prices.

There will be weekly tutorial sessions, starting in the second week of term.

Prerequisites: F79SP1 and F79DF2 (or equivalent).

Books:M. Baxter & A. Rennie, Financial Calculus (CUP, 1996);R. Durrett, Stochastic Calculus (CRC Press);J. Hull, Options, Futures and Other Derivative Securities, 3rd/4th ed. (Prentice Hall,1996);B. Oksendal, Stochastic Differential Equations (Springer, 1998);D. Williams, Probability with Martingales (CUP, 1997).

Assessment: 2 hour exam at the end of the 2nd semester.

F70PE1 PENSIONS Lecturers: A.E. Sneddon

Aims: To introduce fundamental practical and technical issues in the actuarial manage-ment of UK occupational pension schemes.

Summary: The foundations of actuarial mathematics have been covered in 2nd and 3rdyear courses. This course takes some of that work and places it in a practical context.

A pension scheme is an arrangement whereby an employer invests money for the benefit ofits employees and their dependents after they retire or on death before retirement. Someobvious questions arising are:

What level of benefit is reasonable?How should the cost of the benefits to the employer be spread out?How should the fund be invested?How can the actuary be certain that the scheme will not run out of money, even ifthe employer does?

The course will discuss benefit design - that is, exactly what benefits could be offered.We will discuss how the actuary can assess the cost of the benefits, including how she/hemight choose the interest, inflation, salary and service table assumptions necessary. We willdiscuss investment principles and practice for pension schemes, and we will cover brieflythe tax and legislation issues relevant to UK pension schemes.

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While some of the work will be technical in nature, we will also consider some more generalissues surrounding pension schemes, including monitoring pensions issues currently in thenews. Students will be expected to read the financial press regularly and will be required togive a short presentation to the class on a particular current issue. Most technical actuarialwork involves computers and this course will include regular computer laboratory sessions.

Prerequisites: F70LA1 and F70LB2 (or equivalent).

Assessment: This course and F70LP2 will be examined together in a 3 hour exam (80%)at the end of the 2nd semester. Both courses will have an assessed project (10% each).

F70LP2 LIFE OFFICE PRACTICE Lecturer: A.S. Macdonald

Aims: The aim of this course is to introduce students to the practical issues arising in lifeinsurance and the management of a life insurance company.

Summary: The course covers modern life office practice, e.g. types of policy and therisks to which an office is exposed in writing them (conventional and unitised with-profits,non-profit, unit-linked), premiums, actuarial bases (for premiums, experience and valua-tion), bonus systems for distributing profits, solvency, nature and valuation of assets andliabilities, and asset shares. More advanced topics are also covered, including stochasticmodelling, hedging/matching, reserving requirements, capital requirements, orphan as-sets, financial strength, and guarantees. The course will involve practical work, tutorialand project work. Weekly student presentations will cover issues of current interest in theinsurance industry. Most technical actuarial work involves computers and this course willinclude regular computer laboratory sessions.

Prerequisites: F70LA1 and F70LB2 (or equivalent).

Assessment: This course and F70PE1 will be examined together in a 3 hour exam (80%)at the end of the 2nd semester. Both courses will have an assessed project (10% each).

F70DP2 ADVANCED DERIVATIVE PRICING Lecturer: T.C. Johnson

Aims: The aim of this course is to introduce students to advanced and practical topics inderivative markets, which are essential preparation for a career in the financial industry.This course is available only to students on the BSc in Financial Mathematics.

Summary: The material develops ideas from F70CF1 and F79DF2. The course beginswith a review of some of the key concepts in stochastic calculus. It then moves on toapplying these to the question of stochastic volatility, in pricing exotic options and in theinterest rate markets. Numerical techniques for practical application of the theory arealso covered. The course finishes with a discussion of structured products and syntheticsecurities and associated risk management issues.

Prerequisites: F79SP1 and F79DF2 (or equivalent).

Books:M. Joshi, The Concepts and Practice of Mathematical Finance (CUP, 2003);S. Shreve, Stochastic Calculus for Finance II: Continuous Time Models (Springer,2004).

Assessment: Two hour exam (80%) and project work (20%).

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F71RM1 FINANCIAL RISK MANAGEMENT Lecturer: A.J.G. Cairns

Aims: To provide an introduction to the advanced statistical methods underpinning Fi-nancial Risk Management (FRM) and Enterprise Risk Management (ERM), and a thor-ough grounding in the wide range of risks facing a company. To develop key risk assessmentskills.

Summary: This course will give students an introduction to the risk measurement andmanagement process. We will see how financial institutions are faced with a bewilderingarray of risks of all types. Some of the course will focus on risks that are amenableto rigorous statistical analysis, and the process of selecting a good statistical model forforecasting the future. In isolation, students will already be familiar with the individualcomponents of an analysis. The course pulls all of these together to look at the modellingprocess as a whole and as one part of the bigger risk management cycle. Essential elementsof the learning and feedback process are the computer labs where we turn classroom theoryinto practice.

Prerequisites: F78PB2 and F79PA1 (or equivalent).

Books:M. Crouhy, D. Galai & R. Mark, The Essentials of Risk Management (McGraw Hill,2006),A. J. McNeil, R. Frey, & P. Embrechts, Quantitative Risk Management: Concepts,Techniques and Tools (Princeton University Press, 2005).

Assessment: 2 hour exam (80%) at the end of the 1st semester, project work (20%).

F10MM1 OPTIMISATION Lecturer: L. Banjai

Aims: To present different methods of solving optimisation problems in the areas of linearand nonlinear programming, and classical calculus of variations. In addition, there will bean introduction to numerical methods.

Summary: The syllabus is as follows:1. Introduction: simplified examples of common real world situations leading to optimi-

sation problems.2. Linear programming (optimisation of linear functions subject to linear constraints):

basic theory, simplex method, duality, practical techniques.3. Nonlinear programming (optimisation of nonlinear functions subject to constraints):

Lagrange multipliers, Karush-Kuhn-Tucker optimality conditions, convexity, duality.4. Approximation methods for nonlinear programming: line search methods, gradient

methods, conjugate gradient methods.5. Variational problems: Euler-Lagrange equation, boundary conditions, constraints, in-

troduction to dynamic programming, basic ideas on numerical approximation.

Prerequisites: F18CD1 and F18CF1.

Books: The course is based on the following book:Pedregal, Introduction to Optimization (Springer, 2004).

Assessment: 2 hour exam at the end of the 1st semester.

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F70RT2 RISK THEORY Lecturer: V. Shneer

Aims: To introduce and apply the statistical techniques used in the analysis of insuranceprocesses, in particular for the assessment of premiums for short term insurance contracts,for reserving, and for assessing and managing solvency risk.

Summary: We look at some mathematical/statistical models and techniques which areuseful in insurance, particularly short term insurance (for example motor, household, em-ployers’ liability).

We look at how to find the compound distribution of aggregate claims by combining thefrequency of claims with the distribution of the amounts paid out on individual claims;we will consider how this might be used to set a premium, and how the insurers insurethemselves through reinsurance.

We then study aspects of experience rating, which is a method of setting a premium for apolicy which is affected by the claims history of that policy. We look at experience ratingusing Bayesian credibility theory, and in the context of No Claims Discount systems.

The final three topics covered are:Ruin theory (we consider a stochastic model for the reserves of a general insurer andexamine the probability that the reserves fall below zero),Run-off triangles (we study methods used to determine appropriate reserves for generalinsurance),Simulation.

Prerequisites: F79MA1 (or equivalent).

Assessment: 2 hour exam at the end of the 2nd semester.

F71CM2 CREDIT RISK MODELLING Lecturer: A.J. McNeil

Aims: To introduce students to quantitative models for measuring and managing creditrisk; to provide students with an understanding of the credit risk methodology used in thefinancial industry and the regulatory framework in which the credit risk models operate.

Summary: Topics covered includeintroduction to credit risk: credit-risky instruments, defaults, ratings;Merton’s model of the default of a firm;common industry models (KMV, CreditMetrics, CreditRisk+);modelling dependence between defaults with factor models;mixture models of default;the Basel II regulatory capital formula;calculating the portfolio credit loss distribution;calibration and statistical inference for credit risk models.

Books:A. J. McNeil, R. Frey, & P. Embrechts, Quantitative Risk Management: Concepts,Techniques and Tools (Princeton University Press, 2005),C. Blum, L. Overbeck & C. Wagner, An Introduction to Credit Risk Modelling (Chap-man and Hall, 2003).

Assessment: 2 hour exam.

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F70ST2 STATISTICS SPECIAL TOPIC Lecturer: To be arranged

Students taking this course will be required to attend a taught applied statistics course,or undertake an applied statistics reading programme. In either case, there will be anelement of practical work.

Prerequisites: F79MA1 and F79MB2 (or equivalent).

Assessment: Written project (80%), presentation (20%).

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