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Title: Duality theory for robust utility maximisation
Authors: Bartl, Daniel
Kupper, Michael
Neufeld, Ariel
Keywords: Science::Mathematics
Issue Date: 2021
Source: Bartl, D., Kupper, M. & Neufeld, A. (2021). Duality theory for robust utility maximisation. Finance and Stochastics, 25(3), 469-503.
Journal: Finance and Stochastics
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 line. Our results are inspired by – and can be seen as the robust analogues of – the seminal work of Kramkov and Schachermayer (Ann. Appl. Probab. 9:904–950, 1999). 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.
ISSN: 0949-2984
DOI: 10.1007/s00780-021-00455-6
Rights: © 2021 The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature. All rights reserved.
Fulltext Permission: none
Fulltext Availability: No Fulltext
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