## Duality theory for robust utility maximisation

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2021
Neufeld, Ariel
Journal article
Published
##### Published in
Finance and Stochastics ; 25 (2021), 3. - pp. 469-503. - Springer. - ISSN 0949-2984. - eISSN 1432-1122
##### 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.
510 Mathematics
##### Cite This
ISO 690BARTL, Daniel, Michael KUPPER, Ariel NEUFELD, 2021. Duality theory for robust utility maximisation. In: Finance and Stochastics. Springer. 25(3), pp. 469-503. ISSN 0949-2984. eISSN 1432-1122. Available under: doi: 10.1007/s00780-021-00455-6
BibTex
@article{Bartl2021Duali-54230,
year={2021},
doi={10.1007/s00780-021-00455-6},
title={Duality theory for robust utility maximisation},
number={3},
volume={25},
issn={0949-2984},
journal={Finance and Stochastics},
pages={469--503},
author={Bartl, Daniel and Kupper, Michael and Neufeld, Ariel}
}

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Yes
Yes