A stochastic theory of life insurance

A theory of life insurance is considered in which the interest rate is variable and the random fluctuations in the collective are taken into account. The theory explicitly includes a description of how the benefits are changed depending on these factors. A linear feedback which adapts the benefits to the surplus is necessary in order to stabilize the system in the sense that the variance of the surplus remains bounded. Martingale decomposition is a useful tool for the analysis of the fluctuations.