Convex duality and Orlicz spaces in expected utility maximization

摘要

In this paper, we report further progress toward 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 a new economic insight into the nature of primal optima and providing a fresh perspective on the classical papers of Kramkov and Schachermayer. The analysis points to an intriguing interplay between no-arbitrage conditions and standard convex optimization and motivates the study of the fundamental theorem of asset pricing for Orlicz tame strategies.