Optimal Consumption and Investment for Exponential Utility Function

Abstract

We investigate an optimal consumption and investment problem for Black-Scholes type financial market on the whole investment interval [0, T]. We formulate various utility maximization problem, which can be solved explicitly. The method of solution uses the convex dual function (Legendre transform) of the utility function. Related to this concept, we introduce and study the convex dual of the value function for our problem.