Optimal investment strategy for DC pension plan with inflation risk under the hybrid stochastic volatility model

In this paper, we investigate an optimal investment strategy for defined-contribution (DC) pension plan under hybrid stochastic volatility (Heston-Hull-White) model, taking account of the inflation risk and the stochastic salary. The fund wealth is invested in financial market consisting of a risk-free asset, an inflation-indexed bond and a stock with hybrid Heston-Hull-White model. The goal of the pension fund manager is to maximize the expected utility of the terminal real wealth. We derive the Hamilton-Jacobi-Bellman (HJB) equation through the dynamic programming principle, under the constant relative risk aversion (CRRA) utility function, the optimal investment strategy is obtained. Finally, a numerical example is presented to characterize the impacts of financial parameters on the optimal investment strategy.