We study the asset allocation problem for a pension fund which maximizes the expected present value of its wealth augmented by the prospective mathematical reserve at the death time of a representative member. We apply the stochastic optimization technique in continuous time. In order to present an explicit solution we consider the case of both deterministic interest rate and market price of risk.We demonstrate that the optimal portfolio is always less risky than the Merton’s (1969-1971) one. In particular, the asset allocation is less and less risky until the pension date while, after retirement of the fund’s representative member, it becomes riskier and riskier. The paper shows the best way for managing a pension fund portfolio during both the accumulation and the decumulation phases. The paper fills a gap in the optimal portfolio literature about the joint analysis of both the actuarial and the financial framework. In particular, we show that the actuarial part strongly affects the behaviour of the optimal asset allocation.

Keywords : pension fund, mortality risk, asset allocation, inflation risk.

JEL : G23, G11.
MSC 2000 : 62P05, 91B28, 91B30, 91B70, 93E20.