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.