application of probability theory

8/3/2019 Application of Probability Theory

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Application of Probability Theory

The service of insurance functions on the basic principles of probability or the Law of

Averages.

Life insurance transactions are based on the law of averages and the study of mortality.

Probability- The Law of Averages

Probability is a branch of statistics that deals with the chances of the happening of on

event.

Events are grouped into three categories ,one category pertains to events that are boundto happen ,here the probability is „one', indicating the certainty of the event happening.

Similarly ,in the case of events that will never happen, the probability is „zero‟.

Probability

Priori Probability: There are certain probabilities where the outcomes of which are

known in advance are known as Priori probability. Posteriori Probability: Study of number of samples based on the experience of the past

and analyzing the probability of an event occurring is based on the supportive data. This

empirical study is know as Posteriori Probability .

Law of large numbers

According to law of large numbers ,estimates of probability will be realistic only if exposed to

a large population for trial .As it is not practicality possible to examine the whole population

for data, actuaries resort to statistical interference, which means arriving at certain conclusions

based on the study and interpretation of the historic data.

In the study of large numbers, the accuracy of the estimate will depend on the statistical

dispersion .When studying various samples, actuaries decide on the variance of different sets of

values and arrive at the standard deviation.

Mortality Table

An actuarial table indicating life expectancy and death frequency for a given age, occupation,

etc.

A mortality table that lists the death rates of insured persons of each sex and age group and

excludes data from policies that have been recently underwritten. An ultimate mortality table

also lists the proportion of individual survival from birth to any given age. Insurancecompanies use these tables to price insurance products and ultimately the profitability of these

insurance companies depend upon correct analysis of the table.

Investopedia explains Ultimate Mortality Table

By removing the first few years of life insurance data from the table, the ultimate mortality

table more accurately shows the rate of mortality after removing selection effects. People who

just received life insurance will have usually just had a medical exam and are relatively healthy

and so this table attempts to remove that effect.

The calculation of an ultimate mortality table affects insurance requirement reserves and proper

pricing by insurance companies. Along with death and survival rates amongst age groups

andsexes, mortality tables can also list survival and death rates in relation to weight, ethnicityand region.



In actuarial science, a life table (also called a mortality table or actuarial table) is a table

which shows, for each age, what the probability is that a person of that age will die

before his or her next birthday. From this starting point, a number of inferences can be

derived.

The probability of surviving any particular year of age

Remaining life expectancy for people at different ages

Life tables can be constructed using projections of future mortality rates, but more oftenthey are a snapshot of age-specific mortality rates in the recent past, and do not purport

to be projections. For various reasons, such as advances in medicine, age-specific

mortality rates vary over time.

Life tables are usually constructed separately for men and for women because of their

substantially different mortality rates. Other characteristics can also be used to

distinguish different risks, such as smoking status, occupation, and socio-economic

class.

Life tables can be extended to include other information in addition to mortality, forinstance health information to calculate health expectancy. Health expectancies, of

which disability-free life expectancy (DFLE) and Healthy Life Years (HLY) are the

best-known examples, are the remaining number of years a person can expect to live in

a specific health state, such as free of disability..

Two types of life tables are used to divide the life expectancy into life spent in various

states:

1) Multi-state life tables (also known as increment-decrement life tables) based on

transition rates in and out of the different states and to death.

2) Prevalence-based life tables (also known as the Sullivan method) based on external

information on the proportion in each state.

Mortality tables are one of the main tools for the life insurance industry. Mortality

tables are mathematically complex grids of numbers that show the probability of mortality, or death, for members of a certain population within a defined period of time.

Actuarial valuation

The Actuarial valuation of life insurance product is explained along with the concept of

actuarial science, premium and the role of actuaries in the business of life insurance and the

procedure of actuarial valuation.

Role of actuaries in Life Insurance

A crucial role of the actuary is the management of asset liability risk that is critical to financial

institutions.

The actuaries play a major role in analyzing and modeling of problems in finance, risk

management and product designing extensively in the areas of insurance, pensions, investment

and more recently in wider fields such as project management, banking and health care.

Role of actuaries

Actuaries perform a wide variety of roles such as design and pricing of product, financial

management and corporate planning. Actuaries are invariably involved in the overall

management of insurance companies and pension, gratuity and other employee benefit fundsschemes; they have statutory roles in insurance and employee benefit valuations to some extent

in social insurance schemes sponsored by government.



Duties

Actuaries make financial sense of the future: Actuaries are experts in assessing the financial

impact of tomorrow's uncertain events. They enable financial decisions to be made with more

confidence by:

Analyzing the past.

Modelling the future,

Assessing the risks involved, and

Communicating what the results mean in financial terms.

Actuaries enable more informed decisions: Actuaries add value by enabling businesses

and individuals to make better-informed decisions, with a clearer view of the likely

range of financial outcomes from different future events.

Actuaries balance the interests of all: Actuaries balance their role in business

management with responsibility for safeguarding the financial interests of the public.

The duty of actuaries to consider the public interest is illustrated by their legal

responsibility for protecting the benefits promised by insurance companies and pension

schemes. The profession's code of conduct demands the highest standards of personalintegrity from its members.

Life Insurance

It refers to a contract in which the insurer agrees to pay a specified amount on the death of the

assured or on the expiry of a certain fixed period, which ever is earlier. In consideration of

this, the insurer collects premium from the insured. Since the sum for which a policy is taken is

assured to be paid, whether there is death or not, life insurance is also referred to as life

assurance.

Life Insurance history in India

1818:The British introduce life insurance to India, with the establishment of the Oriental Life

Insurance Company in Calcutta.

1870:Bombay Mutual Life Assurance Society is the first Indian owned life insurer.

1912: The Indian Life Assurance Companies Act enacted to regulate the life insurance

business.

1928: The Indian Insurance Companies Act enacted to enable the government to collect

statistical information about both life and non-life insurance businesses.

Life Insurance

1938: The Insurance Act which forms the basis for the most current insurance laws, replaces

earlier Act.

1956: Life Insurance Nationalized: government takes over 245 Indian and foreign insurers and

provident societies.

1956: Government sets up Life Insurance Corporation of India.

1993:Malhotra Committee, headed by former RBI Governor R.N.Malhotra, set up to draw up a

blue print for insurance sector reforms.

Life Insurance



1994:Malhotra Committee recommends re-entry of private player, autonomy to Public Sector

Units insurers.

1997:Insurance regulator IRDA (Insurance regulatory and development authority) set up.

2000:IRDA starts giving licenses to private insurers; ICICI Prudential and HDFC Standard

Life, first private life insurers to sell Insurance policies.

2002: Banks allowed to sell insurance plans.

Life insurance products

The two basic needs applicable universally to all individuals are:

1. Risk coverage and

2. Savings for future.

Risk coverage: Risk is used here to mean “death”. The first basic need is to provide a lumpsum amount to the family in the event of the untimely death of the bread winner. This is called

term insurance or temporary insurance. The lumpsum amount is payable only if the death of

the insured occurs during a selected period. If the insured survives till the end of the selected

period, nothing becomes payable.

Savings for future: Savings is accumulation of funds for a specific purpose in the future. Here

the lump sum insurance amount is payable only if the insured survives till the end of the

selected period. If the insured dies during the period of insurance, nothing becomes payable.

This is called “pure endowment”.

Basic Building Blocks

These two concepts term insurance and pure endowment are the basic elements of every life

insurance product. By combining these two elements in different proportions different products

of life insurance are developed, and the proportion of these two elements in the mixture

depends on the different needs of individuals. These two elements are therefore called the

“Basic Building Blocks” in all life insurance product design.

The life insurance policies developed based on the basic building blocks can be divided on the

basis of

Methods of premium payments,

Single premium policy

Level premium policy

Participation in profit,

With profit policy

Without profit policy

Number of lives covered,

Single life policy

Multiple life policy



Joint life policies

Method of payment of sum assured,

Installments or annuity policies

Lump-sum policies


basis of

Duration of policy

Methods of duration

Whole life policy

Limited payment Whole life policy

Convertible Whole life policy

Methods of Term Insurance

Temporary assurance policy

Renewable term policies

Convertible term policies


basis of

Methods of Endowment

Pure endowment policy

Ordinary endowment policy

Joint endowment policy

Double endowment policy

Fixed term endowment policy

Educational annuity policy

Triple benefit policy

Anticipated endowment policy

Multi purpose endowment policy

Children‟s deferred endowment policy

Money back plans

Annuity plans

Market linked insurance plans



Types of Product

The above types of products offered are categorized as follows:

Pure insurance products - Term plans.

Pure investment products - Pension plans.

Investment cum insurance products - Endowment plan, Money-back plan, Whole-life and

Unit Linked insurance plans.

Risk Commencement

The risk is covered after realization of the premium

Expired and Unexpired Risks: For life it is always the full value.

In non-life the period expired is expired risk. For the balance the insurer creates

Unexpired Risk Reserve (URR). Business net of reinsurance ceded is recognized as Net Written Business . For balance

sheet purposes the premium outgo for reinsurance is deducted to arrive the premium on

Net written business.

Net earned premium= Net written premium – unearned premium Reserve carried

forward to the succeeding fiscal

Sum Assured

This is one of the important components of insurance.

In the case of life it is the value for which it is insured.

In the case of non-life, it is normally the market value for which the insurance is taken.

The claim is settled based on the pro rata average clause. i.e. ratio of the value of the

damaged property to the total value of the asset

In case of some properties where it is difficult to value it, such properties are covered

under Valued Policy based on acceptable certificate of valuation.- normally life

insurance policies

Backdating of Policies

Backdating is permitted within the financial year only. Not earlier than that.

Back dating is resorted to accommodate late birds.

It is also done to accommodate professionals whose business is seasonal.

While backdating the difference between the possible higher premium and the actualpremium is lost by the insurer. But interest is collected.

In general insurance the policy becomes void ab initio if premium is not received. In

Life policies it depends upon policy conditions



Major concepts of Insurance

Major types of hazards:

Moral hazard: certain undesirable pre-dispositions on the part of the insured, adding tothe chance of risk and increases the liability of the insurer.- ex. Smoking hazard

Morale hazard: Careless attitude, dishonest tendency adding to the loss and increasing

the liability of the insurer- a tendency to be careless,for ex. Employee antecedent non-

verification

Occupational Hazard: Occupation of a fireman or a life guard on the beach

Physical hazard: Physical conditions contributing to the enhancement of risk- ex. rain

hazard

application of probability theory

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