Stochastic analysis of life insurance surplus

- The paper is concerned with the evaluation of life insurance surplus.
- A methodology to study stochastic behavior of surplus is proposed.
- The methodology is illustrated on homogeneous portfolios of life insurance policies.
- The analysis is done in the environment of stochastic mortality experience and interest rates.

The aim of the paper is to examine the behavior of insurance surplus over time for a portfolio of homogeneous life policies. We distinguish between stochastic and accounting surpluses and derive their first two moments. A recursive formula is proposed for calculating the distribution function of the accounting surplus. We then examine the probability that the accounting surplus becomes negative in a given insurance year. Numerical examples illustrate the results for portfolios of temporary and endowment life policies assuming a conditional AR(1) process for the rates of return.