Optimal investment strategy for a DC pension plan with mispricing under the Heston model

Abstract

In this article, we consider the optimal investment problem for a defined contribution (DC) pension plan with mispricing. We assume that the pension funds are allowed to invest in a risk-free asset, a market index, and a risky asset with mispricing, i.e. the prices are inconsistent in different financial markets. Assuming that the price process of the risky asset follows the Heston model, the manager of the pension fund aims to maximize the expected utility for the power utility function of terminal wealth. By applying stochastic control theory, we establish the corresponding Hamilton-Jacobi-Bellman (HJB) equation. And the optimal investment strategy is obtained for the power utility function explicitly. Finally, numerical examples are provided to analyze effects of parameters on the optimal strategy.

Keywords:

• Pension investment
• Heston model
• mispricing
• Hamilton-Jacobi-Bellman (HJB) equation
• power utility
• utility maximization

Additional information

Funding

The authors would be very grateful to referee for their suggestions and this research was supported by the National Natural Science Foundation of China under Grant (Nos. 11771329, 11871052).