Optimal Investment Strategy for DC Pension Plan with Stochastic Income and Inflation Risk under the Ornstein–Uhlenbeck Model

Abstract

This paper is concerned with the optimal investment strategy for a defined contribution (DC) pension plan. We assumed that the financial market consists of a risk-free asset and a risky asset, where the risky asset is subject to the Ornstein–Uhlenbeck (O-U) process, and stochastic income and inflation risk were also considered in the model. We firstly derived the Hamilton–Jacobi–Bellman (HJB) equation through the stochastic control method. Secondly, under the logarithmic utility function, the closed-form solution of optimal asset allocation was obtained by using the Legendre transform method. Finally, we give several numerical examples and a financial analysis.

Keywords

• DC pension plan
• O-U process
• HJB equation
• inflation risk
• Legendre transform