Optimal Discounted Portfolio, Expected Wealth and Strategic Consumption for a Defined Contribution Pension Scheme

Abstract

This paper deals with optimal discounted portfolio, expected wealth and strategic consumption process for a defined contribution (DC) pension scheme. The aims of this paper are to find: the optimal discounted portfolio and optimal discounted consumption choice to be adopted by the pension plan member (PPM) up to retirement period; the expected discounted wealth and variance of the expected wealth for the plan member. The financial market is composed by a riskless and a risky assets, and the effective salary of the plan member is assume to be stochastic. The expected discounted wealth and its variance are obtained. The discounted portfolio and consumption processes of the plan member are obtained. It is find that part of the discounted portfolio value is proportional to the ratio of the present value of the discounted expected future contributions to the optimal discounted wealth value overtime. It is also find that there is the need for gradual transfer of part of the portfolio value in risky asset to the riskless one against unforeseen shocks.