Convex Duality and Orlicz Spaces in Expected Utility Maximization

Mathematical Finance 30(1), 85-127, 2020

46 Pages Posted: 30 Nov 2017 Last revised: 6 Jan 2020

See all articles by Sara Biagini

Sara Biagini

LUISS University

Aleš Černý

Bayes Business School (formerly Cass), City, University of London

Date Written: November 24, 2017

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

Suggested Citation

Biagini, Sara and Černý, Aleš, Convex Duality and Orlicz Spaces in Expected Utility Maximization (November 24, 2017). Mathematical Finance 30(1), 85-127, 2020, Available at SSRN: https://ssrn.com/abstract=3078111 or http://dx.doi.org/10.2139/ssrn.3078111

Sara Biagini

LUISS University ( email )

Viale Romania 32
Rome, 00197
Italy

Aleš Černý (Contact Author)

Bayes Business School (formerly Cass), City, University of London

Northampton Square
London, EC1V 0HB
United Kingdom

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