The Application Of Stochastic Analysis In Actuarial Science

The purpose of this paper is to introduce the application of stochastic analysis in actuarial science, especially for life insurance. First, we introduce counting processes and indicator processes to describe the simple insurance policy, which have only two states - live and dead. Then we sketch the Markov chain model for the multi-state insurance policy. A model framework where the traditional set-up is extended by letting the experience basis (interest) be stochastic. The discussion of reserves and surplus are introduced in the following ways: At the outset the premium is set accordingly, on a first order basis, which is a set of hypothetical assumptions about interest, intensities of transition between policy states, costs,and possibly other relevant elements. The first order model is a mean of prudent calculation of premiums and reserves, and its elements are therefore placed to the safe side in a sense that will be made precise later. As time passes, reality reveals true elements that ultimately set the realistic scenario for the entire term of the policy and constitute what is called the second order basis. Upon identifying reserves of first and second order, one obtains an expression for the surplus showing how it stems in the individual technical elements. Numerical illustrations are provided.