BFS 2002

Contributed Talk

Optimal solutions to utility maximization and to the dual problem

Marco Frittelli

We consider increasing strictly concave utility functions that are finite valued on the whole real line and a continuous-time model of a financial incomplete market where asset price processes are semimartingales. We show that if the conjugate of the utility function satisfies a rather weak assumption, then there exists an optimal solution to utility maximization from terminal wealth and to the dual problem of the minimization of generalized divergence distances. This assumption is shown to be equivalent to the condition of reasonable asymptotic elasticity of the utility function, as defined by Schachermayer (1999). The proof is based on a direct application of the properties of the solution of the dual problem.