Duality theory for robust utility maximisation

Daniel Bartl; Michael Kupper; Ariel Neufeld

doi:10.1007/s00780-021-00455-6

Duality theory for robust utility maximisation

Daniel Bartl, Michael Kupper, Ariel Neufeld^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

12 Citations (Scopus)

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.

Original language	English
Pages (from-to)	469-503
Number of pages	35
Journal	Finance and Stochastics
Volume	25
Issue number	3
DOIs	https://doi.org/10.1007/s00780-021-00455-6
Publication status	Published - Jul 2021
Externally published	Yes

Bibliographical note

Publisher Copyright:
© 2021, The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.

ASJC Scopus Subject Areas

Statistics and Probability
Finance
Statistics, Probability and Uncertainty

Keywords

Bipolar theorem
Drift and volatility uncertainty
Duality theory
Robust utility maximisation

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10.1007/s00780-021-00455-6

Cite this

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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.",

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AU - Kupper, Michael

AU - Neufeld, Ariel

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AB - 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.

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KW - Drift and volatility uncertainty

KW - Duality theory

KW - Robust utility maximisation

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Duality theory for robust utility maximisation

Abstract

Bibliographical note

ASJC Scopus Subject Areas

Keywords

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