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Convex duality and Orlicz spaces in expected utility maximization

Biagini, S. and Černý, A. ORCID: 0000-0001-5583-6516 (2018). Convex duality and Orlicz spaces in expected utility maximization. Mathematical Finance,

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.

Publication Type: Article
Additional Information: This is the peer reviewed version of the following article: Biagini, S. and Černý, A. (2018). Convex duality and Orlicz spaces in expected utility maximization. Mathematical Finance, which has been published in final form at http://onlinelibrary.wiley.com/journal/10.1111/(ISSN)1467-9965. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Use of Self-Archived Versions.
Publisher Keywords: utility maximization, Orlicz space, Fenchel duality, supermartingale deflator, effective market completion
Subjects: H Social Sciences > HG Finance
Departments: Cass Business School > Finance
URI: http://openaccess.city.ac.uk/id/eprint/21050
[img] Text - Accepted Version
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