Duality Theory for Robust Utility Maximisation

Daniel Bartl, Michael Kupper and Ariel Neufeld

Papers from arXiv.org

Abstract: In this paper we present a duality theory for the robust utility maximisation problem in continuous time for utility functions defined on the positive real axis. Our results are inspired by -- and can be seen as the robust analogues of -- the seminal work of Kramkov & Schachermayer [18]. Namely, we show that if the set of attainable trading outcomes and the set of pricing measures satisfy a bipolar relation, then the utility maximisation problem is in duality with a conjugate problem. We further discuss the existence of optimal trading strategies. In particular, our general results include the case of logarithmic and power utility, and they apply to drift and volatility uncertainty.

Date: 2020-07, Revised 2021-06
New Economics Papers: this item is included in nep-upt
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Citations: View citations in EconPapers (10)

Published in Finance and Stochastics, 2021+

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Persistent link: https://EconPapers.repec.org/RePEc:arx:papers:2007.08376

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