Optimization of investment strategies for a Defined Contribution (DC) plan member with Couple Risky Assets, Tax and Proportional Administrative Fee

Abstract

Edikan E. Akpanibah and  Udeme O. Ini

The aim of this paper is to study the optimal investment plans of a member in a defined contribution (DC) pension scheme with proportional administrative fee and tax on invested funds under logarithm utility function and Ornstein-Uhlenbeck (O-U) model. This is done by considering a portfolio consisting of a risk-free asset (bank security) and two risky assets (stocks) where the stock market prices are driven by the Ornstein-Uhlenbeck (O-U) process. An optimization problem known as the Hamilton Jacobi Bellman (HJB) equation is obtained by maximizing the expected utility of the member’s terminal wealth. Since the HJB equation is a nonlinear partial differential equation (PDE) and could be complex to solve, we use the Legendre transformation method and dual theory to reduce it to a linear PDE. By method of variable change and separation of variable, closed form solutions of the optimal investment plans are obtained using logarithm utility function. More so, sensitivity analysis of some parameters are carried out theoretically on the optimal investment plans with observations that apart from the changes experienced in the stock market prices caused by the O-U process, the optimal investment plans for the risky assets are inversely proportional to the contribution rate, tax rate imposed on the invested fund, proportional administration fee, investment time, but directly proportional to the appreciation rate of the risky assets.