This paper investigates a Constant Relative Risk Aversion (CRRA) investor as a representative of pension plan participants, who has a finite investment horizon and is subject to the proportional transaction costs and a constant rate of return. We attempt 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. A zero value of the volatility resulted to the value function equals zero and its unit value with the drift parameter ξ equals the discount rate k (ξ=k ) led to the value function becoming indeterminate. Precise conditions are obtained which determine the growth rate of the value function in the sell and buy regions.
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