Mean-Variance Portfolio Selection Problem with Stochastic Salary for a Defined Contribution Pension Scheme: A Stochastic Linear-Quadratic Framework

This paper examines a mean-variance portfolio selection problem with stochastic salary and inflation protection strategy in the accumulation phase of a defined contribution (DC) pension plan. The utility function is assumed to be quadratic. It was assumed that the flow of contributions made by the pension plan members (PPMs) are invested into a market that is characterized by a cash account, an inflation-linked bond and a stock. In this paper, inflation-linked bond is traded and used to hedge inflation risks associated with the investment. The aim of this paper is to maximize the expected final wealth and minimize its variance. Efficient frontier for the three classes of assets that will enable PPMs to decide their own wealth and risk in their investment profile at retirement was obtained. The efficient frontier was found to be parabolic in shape, due to the present of initial capital and the existence of stochastic contributions of the PPM. Some numerical illustration of the analytical results are established in this paper.