Duality theory for robust utility maximisation
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. Prob...
| Main Authors: | , , |
|---|---|
| Other Authors: | |
| Format: | Journal Article |
| Language: | English |
| Published: |
2022
|
| Subjects: | |
| Online Access: | https://hdl.handle.net/10356/162314 |
| _version_ | 1811691077328961536 |
|---|---|
| author | Bartl, Daniel Kupper, Michael Neufeld, Ariel |
| author2 | School of Physical and Mathematical Sciences |
| author_facet | School of Physical and Mathematical Sciences Bartl, Daniel Kupper, Michael Neufeld, Ariel |
| author_sort | Bartl, Daniel |
| collection | NTU |
| description | 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. |
| first_indexed | 2024-10-01T06:14:09Z |
| format | Journal Article |
| id | ntu-10356/162314 |
| institution | Nanyang Technological University |
| language | English |
| last_indexed | 2024-10-01T06:14:09Z |
| publishDate | 2022 |
| record_format | dspace |
| spelling | ntu-10356/1623142022-10-13T04:19:05Z Duality theory for robust utility maximisation Bartl, Daniel Kupper, Michael Neufeld, Ariel School of Physical and Mathematical Sciences Science::Mathematics Bipolar Theorem Drift and Volatility Uncertainty 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. Nanyang Technological University Daniel Bartl is grateful for financial support through the Austrian Science Fund (FWF) under project P28661 and the Vienna Science and Technology Fund (WWTF) under project MA16-021. Ariel Neufeld is grateful for financial support through Nanyang Assistant Professorship Grant (NAP Grant) Machine Learning based Algorithms in Finance and Insurance. 2022-10-13T04:19:05Z 2022-10-13T04:19:05Z 2021 Journal Article Bartl, D., Kupper, M. & Neufeld, A. (2021). Duality theory for robust utility maximisation. Finance and Stochastics, 25(3), 469-503. https://dx.doi.org/10.1007/s00780-021-00455-6 0949-2984 https://hdl.handle.net/10356/162314 10.1007/s00780-021-00455-6 2-s2.0-85107882637 3 25 469 503 en Finance and Stochastics © 2021 The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature. All rights reserved. |
| spellingShingle | Science::Mathematics Bipolar Theorem Drift and Volatility Uncertainty Bartl, Daniel Kupper, Michael Neufeld, Ariel Duality theory for robust utility maximisation |
| title | Duality theory for robust utility maximisation |
| title_full | Duality theory for robust utility maximisation |
| title_fullStr | Duality theory for robust utility maximisation |
| title_full_unstemmed | Duality theory for robust utility maximisation |
| title_short | Duality theory for robust utility maximisation |
| title_sort | duality theory for robust utility maximisation |
| topic | Science::Mathematics Bipolar Theorem Drift and Volatility Uncertainty |
| url | https://hdl.handle.net/10356/162314 |
| work_keys_str_mv | AT bartldaniel dualitytheoryforrobustutilitymaximisation AT kuppermichael dualitytheoryforrobustutilitymaximisation AT neufeldariel dualitytheoryforrobustutilitymaximisation |