1. introduction: why a cimpa-imamis schoolarchive.schools.cimpa.info/anciensite/notescours/... ·...

Report on Cimpa-Imamis School on “Mathematical Finance”

Hanoi, April 24 to May 4, 2007

(Marc Diener and Huyên Pham)

1. Introduction: why a Cimpa-Imamis School This school is one of the 3 schools that have been planned in the IMAMIS program. This European program has its origin in a CIMPA school in 1998 organized in Ho Chi Min City where Professor A. Piriou, now retired, met 10 Filipino mathematicians. To respond to a demand of these Filipino mathematicians, the CIMPA and professor Piriou asked professors F. and M. Diener to apply for an European project, accepted in 2004. The project involves CIMPA through the organization of 3 schools, one in each Asian partners, Malaysia, Vietnam and Philippines. For each of these 3 schools, the EU financial participation is planned to cover 50% of the total cost. The Malaysian school took place in Kuala-Lumpur in May 2006. This is the second school, the third and last one will take place in Ateneo de Manila University in August 2007.

The chosen subjects are topic in Mathematical Finance relevant for teachers and practitioners in Vietnam, Philippines, Malaysia, and other countries in East and South-East Asia. They are topics taught by the lecturers chosen among the most innovative lectures they give in their Master teachings in their home universities.

2. Overview All lectures took place at the Institute of Mathematics, Hanoi (IMH);( the computer sessions took place at an other location.)

The planned lecturers were

Nicole Elkaroui (Polytechnique), Giles Pagès (Paris 6), Santiago Carillio (Autonoma de Madrid), Wolfgang Runggaldier (Padova, Italy), Francine Diener (Nice), Marc Diener (Nice) and Huyên Pham (Paris 7), that, except for Mrs El Karoui that could not come because of personal reason, all gave lectures. Finally, S. Carilio and G. Pagès were assisted by Alberto Suarez and Jacques Printemps respectively, for adding a computer oriented aspect of their lectures. All the talks have been given in English, part with blackboard support part with video-LCD support. All lecturers also provided hands-out of their lecture and all participants could get a copy of all the computer files that had been prepared by the lecturers. The computer programmes given used MatLab (Suarez) and SciLab (Printems)

Expected number of participants was Hanoi: 18, Vietnam (not from Hanoi): 12, ASEAN (not from Vietnam): 13, EU (Lecturers): 8 . Finally, these numbers became 49 people from Hanoi, 14 from Vietnam outside of Hanoi, ASEAN (not in Vietnam) 22, and 8 lecturers. Obviously, the subject attracted many people.

The local Coordinator of the School was Nguyen Dinh Cong (Institute of Mathematics, Hanoi, Deputy Director)

3. The purpose When the writer of these lines began his scientific life, the fact that probability was part of Mathematics was still a matter of dispute; only few French mathematicians were aware of the dramatic progress done in the theory of stochastic process, martingale theory or stochastic integrals, and as a consequence, the teaching of probability at high school was at the best related with combinatorics, or at the worse pure magic.

At the beginning of the 1970� a scientific revolution took place when Black and Scholes (rediscovering results already known by Bachelier) introduced models for the behaviour of stock markets in a way that was enough accurate to diminish dramatically the risks on the so called market of derivatives (such as Put and Call options), and Merton, Harrison and Pliska found out the importance of martingales in modelling these markets, and how to turn the very convincing modelling tool called �arbitrage� into effective mathematical models.

As a consequence, banks and financial institutions became places that would attract the best mathematicians and would issue a demand of production and better understanding of sophisticate new results of math. Moreover, the problem of hedging risks on derivatives gave natural examples of Itô stochastic integrals and martingale representation theorem. Any institution, including the State, that has to deal with exchange rates or interest rates needs to have a full staff that masters the language of martingales and computations of stochastic integrals, creating a demand of young people to be taught these subjects. As usual, the only way for anyone to keep in touch with the evolution of ideas in a subject is to produce oneself results (i.e. do research) in order to enter the exchange process called scientific communication.

When CIMPA asked us to get interested in the Asia Link program of the EU (see next section) it was obvious to us that math for finance could/should be an organising centre for a new impulse in higher order mathematics in South East Asia, as it both involves new beautiful mathematics (martingale theory, stochastic calculus) and existing domain of research (Numerical Methods). Moreover, this domain of mathematical knowledge will be supported by the double demand of teaching and applications, as explained above.

This school is part of the larger project IMAMIS that has been suggested by CIMPA in 2002. This project, that has been worked out mostly by the Université de Nice Sophia-Antipolis (UNSA) and the University of the Philippines (UP), is a training programme for higher order education scholars, and devoted to the creation of 15 new courses in Applied Mathematics and Information Science. These courses build up the knowledge delivered in a new pluri disciplinary masters programme that is organised in three tracks (Mathematical Finance, Numerical Methods, Information Science). It is funded by the Asia Link programme of EU. It is run in partnership with Ateneo De Manila University, Universiti Kebangsaan Malaysia (UKM), Institute of Mathematics Hanoi (IMH), Université de La Rochelle (ULR), Departimento di Mathematica - Universita di Pisa (UniPisa), Universidad Autónoma de Madrid, and Université Pierre et Marie Curie (Paris 6),

As usual in higher order teaching, we found it necessary, besides the creation of the courses, to initiate a research process that would allow the teachers involved to get access to the scientific communication in that domain and thus keep there knowledge up to date after the end of the two-and-a-half years Asia Link support. In our mind, the Cimpa schools are the ideal tool to allow this process.

4. The lectures 1. M. Diener: Discrete-time models in finance (5h) 2. F. Diener: Continuous-time models in finance and stochastic calculus (9h) 3. S. Carrillo and A. Suarez: Operational risk: measurement and control (5h

course + 4h computer) 4. G. Pagès: Introduction to numerical methods in probability for finance (4h

course + 3h computer) 5. J. Printems: Introduction to numerical methods for partial differential

equations in finance (4h course + 3h computer) 6. W. Runggaldier: Interest rate modelling (9h) 7. H. Pham: Portfolio management and option hedging (9h)

1. Discrete-time Models in Finance Marc Diener : University of Nice, [email protected]

http://math1.unice.fr/~diener/

1. Pricing European options in a Cox-Ross-Rubinstein Model. Risque neutral probability. Convergence of the CRR exact formula to the Black-Scholes limit.

2. Pricing American options in a CRR Model. Hedging/superhedging 2. Continuous-time Models in Finance and Stochastic Calculus Francine Diener : University of Nice, [email protected] http://math1.unice.fr/~diener/

1. Brownian motion, Heat equation, Black-Scholes model of stocks prices. Self financing portfolios, stochastic integrals, profit & loss.

2. Ito formula, stochastic differential equations, options pricing in the Black-Scholes model. Delta hedge, vol dependance, limits of the B&S model.

3. The martingal approach or arbitrage pricing theory. 4. Arbitrage free and complet markets: the 2 fondamental theorems

3. Operational risk : measurement and control Santiago Carrillo : RiskLab, Madrid, [email protected] http://www.risklab-madrid.uam.es/es/miembros.html Alberto Suarez : Universidad Autonoma Madrid, [email protected] http://www.risklab-madrid.uam.es/es/miembros.html

I What is operational risk: from thick fingers to rogue traders. 1. basical concepts related to operational risk. 2. the notion of economical capital. 3. the Basel II framework for operational risk. II. Operational risk and Basel II: basic models.

1. the basic indicator approach. 2. the standard approaches. 3. critical analysis of basic model 4. a practical more advanced example: the internal measurement approach.

mailto:[email protected]





http://www.risklab-madrid.uam.es/es/miembros.html


http://www.risklab-madrid.uam.es/es/miembros.html

III. Operational risk and Basel II: advanced models. 1. The loss distribution approach. 2. The choice for severity distribution (threshold effect and Extreme Value

Theory). 3. The frequency distribution. 4. Putting all together: practical computing of economical capital (Panjer

algorithm, FFT and Monte Carlo simulation). IV. Practical issues.

1. using different thresholds 2. using external data. 3. taking into account dependence structure (copula and fat tails).

4. Introduction to numerical methods in probability for finance Gilles Pagès : PMA, University Paris 6, [email protected] http://www.proba.jussieu.fr/pageperso/pages 1. Simulation of random variables, variance reduction 1.1 The fundamental principle of simulation and pseudo-random numbers 1.2 The distribution function method Application to the simulation of exponential and Poisson distributions. 1.3 The rejection method Application to the simulation of normal distributions. 1.4 The Box-Muller method for normal vectors d-dimensional Normal vectors d-dimensional Gaussian vectors (with general covariance matrix). 1.5 Application to the computation of Vanilla options pricing in a Black-Scholes model by Monte Carlo. Premium. Greeks (sensitivity to the option parameters: an elementary approach). 1.6 Variance reduction Control variate (optimization by on-line regression). Symmetrization. Importance sampling. 1.7 Application to European option pricing II Option best match, call on exchange spread. Path-dependent options~I: Asian options. an example of stochastic volatility model: The Heston model. 2. Euler scheme of a Brownian diffusion 2.1 Euler-Maruyama scheme Simulation Strong error rate

Path-dependent options~II: Lookback and barrier options, first approach 2.2 Milshtein scheme 2.3 Weak error of the Euler scheme

Main results for E(f(X_T)) : Talay-Tubaro Theorem, Bally-Talay Theorems Weak error for path-dependent functionals: the Brownian bridges method Application to Path-dependent options~III: partial lookback and barrier options.

Standard Romberg extrapolation and multistep Romberg extrapolation. 3. American options 3.1 From American to Bermuda options 3.2 Dynamic programming formula From arbitrage approaches Optimal stopping theory.


http://www.proba.jussieu.fr/pageperso/pages

Hedging. 3.3 Numerical methods The Longstaff-Schwartz method. The optimal quantization tree approach. On the computer... (3 hours) 4. Simulations on a computer

The students will to compute by themselves some option prices by Monte Carlo simulation.

4.1 European option Compute by Monte Carlo the B-S vanilla Call, best match, exchange spread options as a function of the strike price, without and with control variate, with and without symmetrization.

Idem in a Heston model Barrier options 4.2 American option (in 1-dimension) The Longstaff-Schwartz method. The optimal quantization tree approach. 5. Introduction to numerical methods for partial differential equations in finance

Jacques Printems: LAMA, University Paris 12, [email protected]

http://perso-math.univ-mlv/users/printems.jacques/

1. Partial differential equations in mathematical finance 1.1 Black-Scholes analysis Recall on the derivation of the Black-Scholes PDE

1.2 Examples of some PDE’s occuring in finance with their typical features Through the Black-Scholes model : Large dimensions Degenerate PDE�s (Asian options, Lookback options) Need of numerical tools (no closed forms e.g. : call spread options) Bounded or unbounded domains (barrier options) 1.3 Other methods Stochastic volatility models Heston�s models 2. Finite difference methods for PDE’s

2.1 Basis concepts Derivation of finite difference schemes. Accuracy Notion of stability (time). Explicit and implicit schemes Notion of stability (space). L^\infty-stability and discrete maximum principle

Discretization in higher dimension 2.2 Numerical implementation of BS type equation in 1-dimension.

Numerical proof of the convergence. Numerical rate of convergence. Boundary conditions. Numerical smile.

2.3 Numerical study of a 2-d stochastic volatility model : the Heston model Bring into play the numerical implementation. Sparse storage of the matrices. Comparison of different choices of discretization.

2.4 Technique for reducing the dimension The alternate direction methods : example in a 2-d case The sparse grids

3. American options


http://perso-math.univ-mlv/users/printems.jacques/

3.1 Different formulations The optimal stopping formulation The free boundary formulation The variational inequality formulation

3.2 Semi-discretization in time and numerical methods Comparison of two methods (rate of convergence, efficiency) : Projected gradient method Howard�s method 4. Asian options 4..1 Motivations

4.2 PDE formulation and numerical scheme Rogers and Shi method Numerical implementation

5. Practical work 5.1 European option Computation by Finite difference methods of the BS vanilla call in 1-d, best match in 2-d, exchange spread in 2-d, options as a function of the strike price. Barrier options 4.2 American option (in 1-dimension) The projected gradient method. The Howard method 6. Interest rate modeling

Wolfgang Runggaldier : University of Padova, [email protected]

http://www.math.unipd.it/~runggal/ 1. Bonds and Interest Rates; 2. Short Rate Models; 3. Martingale Models for the Short Rate; 4. Forward Rate Models; 5. Change of Numeraire; 6. LIBOR and Swap Market Models. 7. Portfolio management and option hedging Huyên Pham : PMA University Paris 7, and IUF, [email protected] http://www.proba.jussieu.fr/pageperso/pham/ We present a review of concepts of utility theory and portfolio management in financial markets, and show how stochastic control method are applied in this context:

1. Utility theory and risk aversion 2. Dynamic programming and Bellman approach

Merton�s portfolio/consumption choice, real options � 3. Duality and martingale approach

Mean-variance hedging Quantile hedging


http://www.math.unipd.it/~runggal/


http://www.proba.jussieu.fr/pageperso/pham/

Schedule

Monday 23 April 2007 8h00-9h30 Registration 9h30-10h00 Openning ceremony 10h00-10h15 break 10h15-12h00 M. Diener: Discrete-time models in finance I Afternoon session 13h30-15h00 F. Diener: Continuous-time models in finance and stochastic calculus I. 15h00-15h15 break 15h15-16h45 F. Diener: Continuous-time models in finance and stochastic calculus II. Tuesday 24 April 2007 8h00-9h45 M. Diener: Discrete-time models in finance II 9h45-10h00 break 10h00-12h00 S. Carrillo: Operational risk: measurement and control I Afternoon session 13h30-15h00 S. Carrillo: Operational risk: measurement and control II 15h00-15h15 break 15h15-16h45 S. Carrillo: Operational risk: measurement and control III Wednesday 25 April 2007 8h00-9h15 M. Diener: Discrete-time models in finance III 9h15-9h20 break 9h20-10h30 F. Diener: Continuous-time models in finance and stochastic calculus

IIIa. 10h30-10h40 break 10h40-12h00 F. Diener: Continuous-time models in finance and stochastic calculus

IIIb. Afternoon session 13h30-15h30 A. Suarez: Operational risk I 15h30-15h45 Break 15h45-17h30 A. Suarez: Operational risk II Thursday 26 April 2007 8h00-9h45 F. Diener: Continuous-time models in finance and stochastic calculus

IV. 9h45-10h00 break 10h00-12h00 F. Diener: Continuous-time models in finance and stochastic calculus V. Afternoon session 13h30-15h30 J. Printems: Introduction to numerical methods for partial differential

equations in finance I 15h30-15h45 Break 15h45-17h30 J. Printems: Introduction to numerical methods for partial differential

equations in finance II Friday 27 April 2007 8h30-10h00 J. Printems: Introduction to numerical methods for partial differential

equations in finance III (computer work) 10h00-10h15 Break 10h15-11h45 J. Printems: Introduction to numerical methods for partial differential

equations in finance IV (computer work) Afternoon session 13h30-14h30 G. Pagès: Introduction to numerical methods in probability for finance I14h30-15h00 Break

15h00-16h00 G. Pagès: Introduction to numerical methods in probability for finance II

Saturday 28 April 2007 9h00-10h00 G. Pagès: Introduction to numerical methods in probability for finance

III 10h00-10h30 Break 10h30-11h30 G. Pagès: Introduction to numerical methods in probability for finance

IV Afternoon session (92 Vinh Phuc street, Ba Dinh district, Ha Noi) 13h30-15h00 G. Pagès: Introduction to numerical methods in probability for finance

V (computer work) 15h00-15h15 Break 15h15-16h45 G. Pagès: Introduction to numerical methods in probability for finance

VI (computer work) Wednesday 2 May 2007 8h15-9h45 H. Pham: Portfolio management and option hedging I 9h45-10h00 break 10h00-11h30 H. Pham: Portfolio management and option hedging II Afternoon session 13h30-15h00 W. Runggaldier: Interest rate modelling I 15h00-15h15 Break 15h15-16h45 W. Runggaldier: Interest rate modelling II Thursday 3 May 2007 8h15-9h45 W. Runggaldier: Interest rate modelling III 9h45-10h00 break 10h00-11h30 W. Runggaldier: Interest rate modelling IV Afternoon session 13h30-15h00 H. Pham: Portfolio management and option hedging III 15h00-15h15 Break 15h15-16h45 H. Pham: Portfolio management and option hedging IV Friday 4 May 2007 8h15-9h45 H. Pham: Portfolio management and option hedging V 9h45-10h00 break 10h00-11h30 H. Pham: Portfolio management and option hedging VI Afternoon session 13h30-15h00 W. Runggaldier: Interest rate modelling V 15h00-15h15 Break 15h15-16h45 W. Runggaldier: Interest rate modelling VI 16h45-17h00 Closing of the School

5. Other activities Tuesday 24 April: dinner at family Nguyen Van Duc�s Snake Restaurant in Gia Lam. A delicious opportunity to taste seven different ways to enjoy snake meat and bones. When arriving, participants could see the slaughtering of a snake, a dangerous and not so easy task. This provided also a wonderful opportunity to visit a traditional building Monday 30 April and 1st of May are National holidays in Vietnam. This is why there was no break on Wednesdays and that collective tourism was took place on these days, together with Sunday.

Here an overview of this less scientific aspect of the School, that provided nevertheless the opportunities of many discussions during the trips in bus, boats, and walks through the National Parc. Sunday 29 April � Monday 30 April 2007 Halong � Catba Island tour: bus to Haiphong, express-boat to Catba, walk through Catba National Parc: most came back completely soaked out by the rain but everybody was happy. Lunch at the Prince Hotel, swimming in the bay. Bus to the Noth of the island, where participants to place in dragon-shaped boats. The leave at sunset from Catba island will certainly one of the touristic climax of this tour that nobody will forget. Diner and night at the luxury Mithrin hotel. Next day, travel through the famous islands of Halong Bay with visit to one of the spectacular caves hidden in them. Visit to a small floating fish farms. See food on the boat heading back to Halong, bus travel back to Hanoi. Tuesday 1 May 2007 City tour: Temple of Literature, Tran Quoc Pagoda and Bat Trang Pottery Village. The temple of Literature gave a good opportunity to get in touch with one of the origins of merit bases access to knowledge. Thursday 3 May: closing banquet at Nikko hotel. After the sumptuous dinner, several participants offered spontaneous song performances that enjoyed everybody. Friday 4 May 2007: Visit to Trang An Securities Joint Stock Company. This visit involved only three participants of the school: Lưu Hoàng Đức, Francine Diener and Marc Diener. This gave us the opportunity to have a better understanding of the present (and rapidly changing) state of Securities exchanges in the country.

6. List of Participants 1. Participants

Nr Name Affiliation (in Vietnamese) Affiliation (in English) Nationality (i) Vietnamese participants

1 Nguyễn Thị Thúy Anh ĐHKHTN Hà Nội

College of Natural Sciences, Vietnam National Univ.-Hanoi VIETNAM

2 Nguyễn Thị Ngọc Anh Đại học Bách Khoa Hà nội Hanoi University of Technology VIETNAM

3 Tran Kim Anh DH Nong Nghiep I Hanoi University of Argiculture VIETNAM

4 Tạ Quốc Bảo Đại học Thái Nguyên Thai Nguyen University VIETNAM

5 Phạm Trí Cao Đại học Kinh tế TPHCM University of Economics, Hochiminh City VIETNAM

6 Đặng Đình Châu Đại học KHTN Hà Nội


7 Nguyễn Trung Chính Đại học Ngoại Thương Foreign Trade University, Hanoi VIETNAM

8 Nguyễn Đình Công Viện Toán học

Institute of Mathematics, Vietnamese Acad. Sci. & Tech. VIETNAM

9 Ngô Thế Công Trường Trung học Cơ sở Nguyen Trai High VIETNAM

Nguyễn Trãi School, Hanoi

10 Đỗ Văn Cường

Đại hoc Khoa học Tự nhiên - Đại hoc Quốc gia Hà Nội


11 Ngô Kiên Cường Đại học kinh tế Huế College of Economics, Hue University VIETNAM

12 Trần Mạnh Cường ĐHKHTN - ĐHQGHN


13 Nguyễn Quang Cường Đại học Duy Tân Duy Tan University, Danang VIETNAM

14 Đỗ Ngọc Diệp Viện Toán học


15 Nguyễn Tiến Dũng

Đại học KHTN-ĐHQG Hà Nội


16 Lưu Hoàng Đức Viện Toán học


17 Trần Anh Đức Viện Toán học


18 Võ Thị Trúc Giang ĐẠI HỌC TIỀN GIANG Tien Giang University VIETNAM

19 Đặng Vũ Giang Viện Toán Học


20 Nguyễn Thị Hà Đại học Nha Trang Nha Trang University VIETNAM

21 Vũ Thị Hiền

Đại học KHTN-DDHQG Hà Nội


22 Đỗ Văn Hiệp Viện Toán Học


23 Dương Mạnh Hồng Viện Toán học


24 Trần Minh Hoàng Đại học Bách khoa Hà nội Hanoi University of Technology VIETNAM

25 Đỗ Thị Thu Hường Học Viện Tài Chính Academy of Finance, Hanoi VIETNAM

26 Phan Thị Hương Học Viện Kỹ thuật Quân sựMilitary Academy of Technology VIETNAM

27 Nguyễn Thị Mai Hương Học viên Cao học K13 VTH


28 Nguyễn Văn Hữu

Khoa Toán-Cơ-Tin học, ĐHKHTN


29 Phạm Văn Khánh Học Viện Kỹ thuật Quân sựMilitary Academy of Technology VIETNAM

30 Phạm Quang Khoái Đại học Lâm Nghiệp Vietnam Forest University, Hà Tây VIETNAM

31 Bùi Thị Hà Linh Học Viện Tài Chính Academy of Finance, Hanoi VIETNAM

32 Ngô Hoàng Long ĐHSP Hà Nội Hanoi University of Education VIETNAM

33 Hoàng Đức Mạnh Đại học Kinh tế Quốc dân National Economics University, Hanoi VIETNAM

34 Nguyễn Quang Minh Viện Toán học


35 Trần Minh Ngọc Đại học Khoa học tự nhiên


36 Bùi Nguyễn Trâm Ngọc

Đại học KHTN-Tp Hồ Chí Minh

College of Natural Sciences, Vietnam National Univ.-HCMC VIETNAM

37 Bùi Thị Thanh Nhàn Đại học Quy Nhơn Quy Nhon University VIETNAM

38 Đặng Thị Tố Như Trường Đại hoc Kinh tế Đà Nẵng

Danang University of Economics VIETNAM

39 Nguyễn Hồng Nhung Đại học Hoa Sen Thành phố Hồ Chí Minh

Hoa Sen University, Ho Chi Minh City VIETNAM

40 Hồ Đăng Phúc Viện Toán học


41 Tạ Duy Phượng Viện Toán học


42 Trần Văn Quý ĐHThái Nguyên Thai Nguyen University VIETNAM

43 Thiều Lê Quyên Học Viện Kỹ thuật Quân sựMilitary Academy of Technology VIETNAM

44 Nguyễn Thị Thúy Quỳnh Học viện Tài chính Academy of Finance, Hanoi VIETNAM

45 Nhan Anh Thai Trường Đại hoc Cần Thơ School of Education, Can Tho University VIETNAM

46 Nguyễn Hữu Thái ĐH Kinh tế TP Hồ Chí Minh

University of Economics, Hochiminh City VIETNAM

47 Trần Văn Thành Viện Toán học


48 Lê Văn Thành Đại học Vinh Vinh University VIETNAM

49 Hoàng Phương Thảo Học Viện Tài Chính Academy of Finance, Hanoi VIETNAM

50 Trần Hùng Thao Viện Toán học


51 Hoàng Phương Thảo Đại học Khoa hoc Tự nhiên


52 Phạm Minh Thông Đại học Tây Bắc Tay Bac University VIETNAM

53 Nguyễn Thị Thế Đại học Vinh Vinh University VIETNAM

54 Nguyễn Tuấn Thiện Đại học Bách Khoa Hanoi University of Technology VIETNAM

55 Nguyễn Thị Thanh Thuỷ Đại học Sư Phạm Hà Nội Hanoi University of Education VIETNAM

56 Hà Thành Trung Viện Toán học


57 Trần Đình Tuấn Đại học Bách Khoa Hà Nội Hanoi University of Technology VIETNAM

58 Phạm Viết Thanh Tùng Cao đẳng Tài chính Kế toán Quảng Ngãi

College of Financial Accounting, Quang Ngai VIETNAM

59 Trần Gia Tùng Đại học Kinh tế TPHCM University of Economics, Hochiminh City VIETNAM

60 Trâ n Đi nh Tương Cao đăng công đông Ba Ri a Vu ng Ta u

Community College of Baria-Vungtau VIETNAM

61 Trần Đông Xuân Đại học Cần Thơ Can Tho University VIETNAM

62 Tăng Thị Hà Yên Viện Toán học


63 Nguyễn Tiến Yết

Đại hoc Khoa học Tự nhiên - Đại hoc Quốc gia Hà Nội


(i) Non-Vietnam based participants

64 Nguyen Dinh Ha Ecole Polytechnique Ecole Polytechnique, FRANCE VIETNAM

65 Doan Thai Son Vien Toan Hoc Institute of Mathematics, Vietnamese Acad. Sci. & Tech. VIETNAM

66 Ha Huy Thai Economie mathématique Univ. Paris VI, FRANCE VIETNAM

67 Nguyen Trung Lap Univ. de Paris VI Univ. Paris VI, FRANCE VIETNAM

68 Almocera S. Lorna University of the Philippines, Cebu City

University of the Philippines, Cebu City, PHILIPPINES

PHILIPPINES

69 Balila Edwin A Adventist University of Philippines

Adventist University of Philippines, PHILIPPINES

PHILIPPINES

70 Cabral Emmanuel Ateneo de Manilla University, Quezon City

Ateneo de Manilla University, Quezon City, PHILIPPINES

PHILIPPINES

71 Shafiqul Islam University of Dhaka, Dhaka University of Dhaka, BANGLADESH BANGLADESH

72 Uyaco-Catinan Filame Joy College of Science Philippines

College of Science, Quezon City - PHILIPPINES

PHILIPPINES

73 Tuprio Elvira Ateneo de Manilla University

School of Science and Engineering, Quezon PHILIPPINES

City - PHILIPPINES

74 Ramil Tagum Bataller Ateneo de Manilla University

School of Science and Engineering, Quezon City - PHILIPPINES

PHILIPPINES

75 Wee Oliver Ian College of Science University of Philippines, Quezon City - PHILIPPINES

PHILIPPINES

76 Gao Yan University of Shanghai

Uinversity of Shanghai for Science and Technology, Shanghai - CHINA

CHINA

77 Saelim Rattikan Prince of Songkla University, Pattani

Prince of Songkla University, Pattani, THAILAND

THAILAND

78 Hematulin Apichai Nakhonratchasima Rajabhat University

Nakhonratchasima Rajabhat University, Nakhonratchasima - THAILAND

THAILAND

79 Sattayatham Pairote Suranaree University of Technology

Suranaree University of Technology, Muang Nakhon Ratchasima - THAILAND

THAILAND

80 Kachin Goganutaporn Valaya Alongkorn Rajabhat University

Valaya Alongkorn Rajabhat University, Pathumthani � THAILAND

THAILAND

81 Prasangika K.D. University of Ruhuna University of Ruhuna, Matara, SRI-LANKA SRI-LANKA

82 Salleh Hassilah Binti University of Oslo University of Oslo, NORWAY MALAYSIA

83 Visal Hun Royal Academy of CambdiaInstitute of Sc. and Tech, Phnom Penh, CAMBODIA

CAMBODIA

84 Dakila Vine Villan Univ. of the Philippines College

College of Science - University of Philippines,Quezon City - PHILIPPINES

PHILIPPINES

2. Lecturers

Nr Name Institutions Nationality 1 Marc Diener University of Nice FRANCE 2 Francine Diener University of Nice FRANCE 3 Santiago Carrillo RiskLab, Madrid SPAIN 4 Alberto Suarez Universidad Autonoma Madrid SPAIN 5 Gilles Pagès PMA, University Paris 6 FRANCE 6 Jacques Printems LAMA, University Paris 12 FRANCE 7 Wolfgang Runggaldier University of Padova ITALY 8 Huyên Pham PMA University Paris 7, and IUF FRANCE

3. Invited guest participant

Milagros P. Navarro Department of Mathematics, University of the Philippines Diliman, Quezon City 1101 PHILIPPINES 4. Vietnamese invited guests

1. Prof. Nguyễn Khoa Sơn, Vice-President of VAST 2. Prof. Ngô Việt Trung, Director of Institute of Mathematics 3. Prof. Lê Tuấn Hoa, Deputy Director of Institute of Mathematics 4. Prof. Hà Huy Khoái, Former Director of Institute of Mathematics 5. Prof. Hoàng Xuân Phú, Vice-Chairman of the Scientific Council of Institute of

Mathematics 6. Prof. Nguyễn Hữu Dư, Dean of Math. Department of Hanoi University of Sciences Prof. Nguyễn Việt Dũng, Deputy Director of Institute of Mathematics

7. What will be the follow up to the school ? We received many reaction of participants expressing the fact that thanks to this school they understand now that sophisticate mathematics were needed in modern finance.

For those who were already conscious of this evolution this school was a good occasion to see how the most recent topics in finance can be taught at Master level. This gave all the opportunity to build up collaboration schemes. This has already produced an partnership in applying for an Erasmus Mundus Action 4 proposal submitted to the European Commission. If it is accepted, it will allow new meetings in the near future.

This school will also influence the teaching of applied math in the represented countries in the spirit of the International Master in Applied Mathematics and Information Sciences (Imamis).

Thanks to a ForMath Vietnam, several Vietnamese Master students in Europ had the opportunity to have a contact with their home institutions. This school helped them to understand the importance of keeping on studying at a higher level and to engage themselves in a Doctoral programme.

Finally, this school will promote the research on mathematical Finance at the Department of Probability and Statistics of the Institute of Mathematics in Hanoi, as well as collaboration with other academic and educational institutions in Vietnam.

Répartition par nationalité des participants à l'école"Mathematical Finance"

Hanoi (Vietnam), avril-mai 2007

1 1 1 31

8

1

4

64

BANGLADESH 1

CAMBODGE 1

CHINE 1

FRANCE 3

MALAISIE 1

PHILIPPINES 8

SRI LANKA 1

THAILANDE 4

VIETNAM 64

TOTAL = 84

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