A simple numerical solution for an optimal investment strategy for a DC pension plan in a jump diffusion model

Abstract

In this paper, we study an optimal investment strategy for a fund manager of a DC pension who wants to maximise the expected exponential utility of the terminal wealth in a market where the stock is a jump diffusion process. Using stochastic control theory, we derive a Hamilton–Jacobi–Bellman equation. Since the market is not complete, the optimal strategy cannot be found in closed as is done in most literature on DC pension plans. We characterise the optimal strategy as a solution of an integro-ordinary differential equation which can easily be solved by a simple numerical method. We investigate the impact of different jump parameters through numerical experiments using a familiar distribution of jumps.