Management of a pension fund under mortality and financial risks

The purpose of this article is to analyze the dividend policy and the asset allocation of a pension fund. We consider a financial market composed of three assets: cash, stocks and a rolling bond. Interest rates are driven by Vasicek's model whereas the mortality of the insured population is modelled by a Poisson process. We determine investment and dividend policies maximizing the utility of dividends and of terminal surplus under a budget constraint. In particular, solutions are developed for CRRA and CARA utility functions. The methodology is based both on the Cox and Huang's approach and on the dynamic programming principle.