Optimal Defined Contribution Pension Management with Jump Diffusions and Common Shock Dependence

Wujun Lv, Linlin Tian () and Xiaoyi Zhang
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Wujun Lv: College of Science, Donghua University, Shanghai 201620, China
Linlin Tian: College of Science, Donghua University, Shanghai 201620, China
Xiaoyi Zhang: School of Economics and Management, Hebei University of Technology, Tianjin 300401, China

Mathematics, 2023, vol. 11, issue 13, 1-20

Abstract: This work deals with an optimal asset allocation problem for a defined contribution (DC) pension plan during its accumulation phase. The contribution rate is assumed to be proportional to the individual’s salary. The salary follows a Heston stochastic volatility model with jumps, and there exists common shock dependence between the salary and the volatility. Since the time horizon of pension management is quite long, the influence of inflation is considered in the given context. The aim of the pension plan described in this paper is to reduce fluctuations in terminal wealth by investing in the bond and the stock. Through the dynamic programming principle, the Hamilton–Jacobi–Bellman equation is shown. The explicit expression of the investment decision is derived by solving the Hamilton–Jacobi–Bellman equation. In the last part, a numerical analysis is shown to illustrate the impacts of different parameters on the optimal investment policy.

Keywords: DC pension plan; stochastic volatility; Poisson process; common shock dependence; inflation; Hamilton–Jacobi–Bellman equation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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