Investor’s Power Utility Optimization with Consumption, Tax, Dividend and Transaction Cost under Constant Elasticity of Variance Model

This work considered an investor’s portfolio where consumption, taxes, transaction costs and dividends are in
involved, under constant elasticity of variance (CEV). The stock price is assumed to be governed by a constant
elasticity of variance CEV model and the goal is to maximize the expected utility of consumption and terminal
wealth where the investor has a power utility preference. The application of dynamic programming principles,
specifically the maximum principle obtained the Hamilton-Jacobi-Bellman (HJB) equation for the value
function on which elimination of variable dependency was applied to obtain the close form solution of the
optimal investment and consumption strategies. It is found that optimal investment on the risky asset is horizon
dependent