Dynamic mean-variance asset allocation for a DC pension plan with the minimum guarantee under 4/2 stochastic volatility model

This paper investigates the optimal investment problem for the defined contribution (DC) pension plan with 4/2 stochastic volatility the and minimum annuity guarantee in a mean-variance framework. The fund manager is allowed to invest pension wealth in a financial market consisting of a risk-free asset, a zero-coupon bond and a stock, where the interest rate term structure follows the affine interest rate model and the stock price process follows the 4/2 stochastic volatility model with stochastic interest rate. Assuming that the minimum guarantee level is correlated with the instantaneous interest rate, a mean-variance model is developed with the objective of the variance of the surplus process in which the terminal wealth exceeds the minimum guarantee. By constructing an auxiliary process, the initial problem is transformed into an equivalent self-financing investment problem, and closed-form solutions for the efficient strategy and efficient frontier are derived using Lagrange duality theorem and stochastic optimal control theory. Finally, the effects of model parameters on the efficient strategy and efficient frontier are analyzed by numerical examples.