Asymptotic Portfolio Strategy Based on the CEV Model with General Utility Function

Abstract

The optimal investment problem is a hot field of financial risk control. The analytical solution of investment strategy can be obtained with the power function utility and exponential function utility when the stock price obeys the constant elasticity of variance (CEV) model. However, different investors have different risk preferences; it means that different investors have different utility functions. In this paper, we propose an asymptotic analysis method to obtain the asymptotic solution of investment strategy with the general utility function. The value function is expanded in the form of series, the expressions of the zero-order term and first-order term of the series expansion are derived, respectively, and the error between the asymptotic approximation and the optimal value function is calculated. Finally, the numerical examples provide comparative analysis between the analytical solution and the asymptotic solution to verify the effectiveness of the proposed method.