Mathematics in Life Insurance

elective courses

This is a basic course providing theoretical principles for computation of premiums and reserves in a life insurance company. The required mathematical background comprises calculus and the first course in probability. The computational models for individual and multiple - life policies (including multiple - decrement model) are developped in a systematic way. The carefully selected problems and exercises reinforce working knowledge of theoretical issues. The course can serve as a good preparation for future actuaries.

The course Life Insurance Mathematics covers all the basic principles of actuarial computations performed by actuaries in life insurance companies and in governmental regulatory institutions.

The course assumes some aquaitance with calculus, basic probability and theory of interest.

First, the demographic model is developed, which serves during the whole lecture as a main building block. On this basis the single-life insurance model is developed, which covers all issues concerning calculations of premiums and reserves. Both discrete and continuous cases are carefully studied. The continuous model culminates in Thiele differential equation, which describes the evolution of the reserve in time. The first important generalization of the above model comprisesmultiple-life policies. The most important cases are: marriage pension schemes and widows annuities. The second generalization of the classical single-lifemodel allows for multiple decrements (e.g. the insured sum is paid out not only in the case of death but also in case of disability caused by an accident). In order to treat such cases the basic demographic model has to be properly extended. The last but not the least issue concerns the expense - loading of premiums and reserves. It turns out that the basic actuarial equivalence principle can be easily adopted for this "real-life"case.

The integral part of the course are numerous problems and exercises which are carefully selected to inforce good understanding of theoretical issues as well as to promote the practical knowledge od students.

N.L. Bowers et al., Actuarial Mathematics. 2nd ed., The Society of Actuaries, 1997.

H.U. Gerber, Life Insurance Mathematics. Swiss Association of Actuaries, Springer-Verlag, 1997.

A. Neill, Life Contingencies. Heinemann, 1977.

1) student knows the basic notions of demographic model used in actuarial computations.

2) understands thoroughly the notion of actuarial present value; can compute net single premiums for basic insurance policies.

3) can compute actuarial values of basic life annuities

4) knows the the notion of regular (level) premium; can compute premiums paid with different frequencies.

5) understands the basic role of reserve in current controll of balance.

6) knows the basics of multiple life theory.

7) knows how to extend tha equivalence principle to load the net premiums in order to get gross premiums.

the final grade is the weighted average: 25% of the grade from classes and 75% of the result of the final exam.