Optimal investment problem with taxes, dividends and transaction costs under the constant elasticity of variance (CEV) model

This paper studies the optimal investment problem of utility maximization with taxes, dividends and transaction costs under the constant elasticity of variance (CEV) model. The Hamilton-Jacobi-Bellman (HJB) equation associated with the optimization problem is established via stochastic control approach. Applying power transform and variable change technique, we obtain explicit solutions for the logarithmic and exponential utility functions. For the quadratic utility function, we obtain the optimal strategy explicitly via Legendre transform and dual theory. Furthermore, we analyze the properties of the optimal strategies. Finally, a numerical simulation is presented to discuss the effects of market parameters on the strategies. Key–Words: Optimal investment, Transaction cost, Constant elasticity of variance (CEV) model, Utility function, Hamilton-Jacobi-Bellman (HJB) equation, Legendre transform