Continuous Time Mean-Variance Portfolio Selection Problem with Stochastic Salary and Strategic Consumption Planning for a Defined Contribution Pension Scheme

This paper examines a continuoustime mean-variance portfolio selection problem with stochastic salary and strategic consumption planning for a constant relative risk averse (CRRA) pension plan member (PPM) in the accumulation phase of a defined contribution (DC) pension plan. It was assumed that the flow of contributions made by the PPM are invested into a market that is characterized by a cash account, an index bond and a stock. Due to the increasing risk of inflation rate and diminishing value of pension benefits, the need for managing such risk has becomes imperative. In this paper, index bond is traded and used to protect the investment against inflation risks. The aim of this paper are to determine the optimal variational Merton portfolios, optimal variational consumption plan for a lifecycle of a PPM and to maximize the expected final value of wealth and simultaneously minimize its variance and consumption risk. Efficient frontier for the three classes of assets that will enable PPMs to decide their own value of wealth and risk in their investment profile at retirement was obtained. The optimal consumption overtime and final consumption of the PPM are established. The variational portfolio processes for the three classes of assets were established. Some numerical results are also consider in this paper.