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Finance and Stochastics

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14-06-2021

Duality theory for robust utility maximisation

Authors: Daniel Bartl, Michael Kupper, Ariel Neufeld

Published in: Finance and Stochastics | Issue 3/2021

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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.

previous article A unified framework for robust modelling of financial markets in discrete time

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Title: Duality theory for robust utility maximisation
Authors: Daniel Bartl
Michael Kupper
Ariel Neufeld
Publication date: 14-06-2021
Publisher: Springer Berlin Heidelberg
Published in: Finance and Stochastics / Issue 3/2021
Print ISSN: 0949-2984
Electronic ISSN: 1432-1122
DOI: https://doi.org/10.1007/s00780-021-00455-6

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