Equilibrium investment strategy for a defined contribution pension plan under stochastic interest rate and stochastic volatility

Abstract This paper aims to find the equilibrium investment strategy for a defined contribution pension plan under the mean–variance criterion where both the interest rate and volatility are stochastic in the financial market. The financial market consists of a risk-free asset, a bond and a risky asset. Specifically, an affine model, which includes the Cox-Ingersoll-Ross model and the Vasicek model as special cases, is used to characterize the stochastic dynamics of the interest rate, and the price process of the risky asset is described by the Heston volatility model. Under the framework of Nash equilibrium, we first define the equilibrium strategy and the equilibrium value function. Then, by solving an extended Hamilton–Jacobi-Bellman equation, we obtain both the equilibrium investment strategy and the corresponding equilibrium value function explicitly. Furthermore, the effects of the stochastic interest rate and the stochastic volatility on the equilibrium investment strategy and the equilibrium efficient frontier are analyzed. Some numerical results and the economic meanings behind are also presented.