Asset allocation for a DC pension fund with stochastic income and mortality risk: A multi-period mean–variance framework

This paper investigates an asset allocation problem for defined contribution pension funds with stochastic income and mortality risk under a multi-period mean–variance framework. Different from most studies in the literature where the expected utility is maximized or the risk measured by the quadratic mean deviation is minimized, we consider synthetically both to enhance the return and to control the risk by the mean–variance criterion. First, we obtain the analytical expressions for the efficient investment strategy and the efficient frontier by adopting the Lagrange dual theory, the state variable transformation technique and the stochastic optimal control method. Then, we discuss some special cases under our model. Finally, a numerical example is presented to illustrate the results obtained in this paper.