An Orlicz Spaces Duality for Utility Maximization in Incomplete Markets

Abstract

Biagini (2004) and Biagini-Frittelli (2005) faced the utility maximization problem in incomplete markets when the price process of financial assets is described by general semimartingales that are not necessarily locally bounded. They introduced a class of well-controlled admissible strategies in this (very) risky context and then they solved the maximization problem with an (L ∞, ba)-duality technique. In this note we almost stick to their setup and we show that their dual result can be obtained via an Orlicz spaces duality, naturally associated with the utility function considered. This new formulation gives additional insight into the nature of the loss control in the good trading strategies.