Lifecycle optimal investment policy for pension funds with transaction costs

Abstract

In this paper,lifecycle investmentof a Constant Relative Risk Aversion (CRRA) investor as a representative of pension plan participants is investigated. The investor has a finite investment horizon and is subject to the proportional transaction costs and a constant rate of return. Attempt is made to maximize the investor’s utility by trading between stock and money market account. A set of partial differential equations are derived and closed form solution proffered. The effects of the volatility of the risky asset are investigated and it shows that a zero value of the volatility resulted to the value function equals zero and its unit value with the drift parameterξ equals the discount rate k, gave an indeterminate value for  the value function. Precise conditions are obtained which determine the growth rate of the value function in the sell and buy regions.