Stochastic pension fund control in the presence of Poisson jumps

Abstract

We consider the problem of optimal funding and asset allocation for a defined benefit pension scheme by assuming that the pension fund can be invested in a risk-free asset and a risky asset whose return follows a jump diffusion process. We extend existing literature which mainly assumes that the risky asset’s return follows a pure diffusion process. In a stochastic analysis of the optimal policies we show that the optimal contribution and asset allocation policies have similar forms as in the pure diffusion approaches, but with a modification for the effect of jumps. These results hold under both constant pension scheme benefit outgo and stochastic pension scheme benefit outgo. Using a sensitivity analysis of the effect of the mean jump magnitude on the asset allocation policy, we show that increasing (in absolute terms) the mean jump magnitude reduces the allocation in the risky asset and increases the allocation in the risk-free asset.