Convex Duality and Orlicz Spaces in Expected Utility Maximization

Abstract

In this paper we report further progress towards a complete theory of state-independent expected utility maximization with semi-martingale price processes for arbitrary utility function. Without any technical assumptions we establish a surprising Fenchel duality result on conjugate Orlicz spaces, offering a new economic insight into the nature of primal optima and providing a fresh perspective on the classical papers of Kramkov and Schachermayer (1999, 2003). The analysis points to an intriguing interplay between no-arbitrage conditions and standard convex optimization and motivates study of the Fundamental Theorem of Asset Pricing (FTAP) for Orlicz tame strategies.

Keywords: utility maximization, Orlicz space, Fenchel duality, supermartingale deflator, effective market completion