Optimal investment strategy with constant absolute risk aversion utility under an extended CEV model

Abstract

In this paper, we develop an extended constant elasticity of variance (CEV) model with stochastic volatility to study an optimal investment strategy problem. This extended CEV model remedies the shortcoming of classical CEV model. In CEV model, the volatility term is an power function of stock price, which only covers firm-specific risks. Consequently, we consider the coefficient of volatility with the mean reverting process to make the volatility involve the market risks to improve the classical CEV model. For the optimal investment objective with a constant absolute risk aversion (CARA) utility function, the analytical solution under the extended CEV model cannot be obtained due to the complicated nonlinearity of the partial differential equation. In this paper we successfully employ a dual method, Legendre transformation, and an asymptotic expansion technique to approach an asymptotic solution. The numerical examples indicate the optimal strategy is an increasing function of the expectation of stock returns and correlations between the two market risks. Besides, it is a decreasing function of interest rate and risk aversion coefficient. In addition, by statistical analysis, we find that the power parameter, the expectation of stock returns and interest rate are all significant factors affecting the investment strategy.