Robust utility maximizing strategies under model uncertainty and their convergence
- In this paper we investigate a utility maximization problem with drift uncertainty in a multivariate continuous-time Black–Scholes type financial market which may be incomplete. We impose a constraint on the admissible strategies that prevents a pure bond investment and we include uncertainty by means of ellipsoidal uncertainty sets for the drift. Our main results consist firstly in finding an explicit representation of the optimal strategy and the worst-case parameter, secondly in proving a minimax theorem that connects our robust utility maximization problem with the corresponding dual problem. Thirdly, we show that, as the degree of model uncertainty increases, the optimal strategy converges to a generalized uniform diversification strategy.
Author: | Jörn SassORCiD, Dorothee WestphalORCiD |
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URN: | urn:nbn:de:hbz:386-kluedo-79062 |
DOI: | https://doi.org/10.1007/s11579-022-00312-w |
ISSN: | 1862-9660 |
Parent Title (English): | Mathematics and Financial Economics |
Publisher: | Springer Nature - Springer |
Document Type: | Article |
Language of publication: | English |
Date of Publication (online): | 2024/03/27 |
Year of first Publication: | 2022 |
Publishing Institution: | Rheinland-Pfälzische Technische Universität Kaiserslautern-Landau |
Date of the Publication (Server): | 2024/03/27 |
Issue: | 16 |
Page Number: | 31 |
First Page: | 367 |
Last Page: | 397 |
Source: | https://link.springer.com/article/10.1007/s11579-022-00312-w |
Faculties / Organisational entities: | Kaiserslautern - Fachbereich Mathematik |
DDC-Cassification: | 5 Naturwissenschaften und Mathematik / 510 Mathematik |
Collections: | Open-Access-Publikationsfonds |
Licence (German): | Zweitveröffentlichung |