Convex duality and Orlicz spaces in expected utility maximization

TL;DR

This paper advances the theory of expected utility maximization in financial markets by establishing a Fenchel duality result on Orlicz spaces, linking no-arbitrage conditions with convex optimization.

Contribution

It introduces a novel Fenchel duality framework on conjugate Orlicz spaces for utility maximization without technical assumptions, offering new economic insights.

Findings

Established a Fenchel duality result on Orlicz spaces

Connected no-arbitrage conditions with convex optimization

Provided a new perspective on classical utility maximization results

Abstract

In this paper 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 a new economic insight into the nature of primal optima and providing 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.