Convex duality and Orlicz spaces in expected utility maximization

We report further progress towards a complete theory of state-independent expected utility maximization with semimartingale price processes for arbitrary utility function. Without any technical assumptions we establish a... [ view full abstract ]

We report further progress towards a complete theory of state-independent expected utility maximization with semimartingale price processes for arbitrary utility function. Without any technical assumptions we establish a surprising Fenchel duality result on conjugate Orlicz spaces, offering fresh perspective on the classical papers of Kramkov and Schachermayer (1999, 2003). This leads to new notion of effective market completion and shows dual optimizer cannot be associated with a supermartingale deflator in general.  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.