Optimal Investment Strategy for Defined Contribution Pension Plans under the CEV Model

Abstract

This paper studies the optimal investment strategy for an investor who seeks to maximize the expected utility of the terminal wealth in a defined contribution pension plan. The portfolio consists of a risk-free asset, and a stock whose price dynamics are governed by a constant elasticity of variance (CEV) model. We derive the explicit solutions for the CARA utility function via power transform technique and variable change method. The solution consists of a moving Merton strategy and a correction factor. The moving Merton strategy represents the classical Merton strategy but with an updated volatility at current time and the correction factor denotes the supplement part resulting from the change of the volatility. Furthermore, in order to better understand the influences of the correction factor on the optimal investment strategy, we examine the property of the correction factor. Finally, we present a numerical simulation to illustrate the dynamic behaviors of the correction factor and the optimal strategy.