Strategies with minimal norm are optimal for expected utility maximization under high model ambiguity
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866929209283182592 |
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| author | Carassus, Laurence Wiesel, Johannes |
| author_facet | Carassus, Laurence Wiesel, Johannes |
| contents | We investigate an expected utility maximization problem under model uncertainty in a one-period financial market. We capture model uncertainty by replacing the baseline model $\mathbb{P}$ with an adverse choice from a Wasserstein ball of radius $k$ around $\mathbb{P}$ in the space of probability measures and consider the corresponding Wasserstein distributionally robust optimization problem. We show that optimal solutions converge to a strategy with minimal norm when uncertainty is increasingly large, i.e. when the radius $k$ tends to infinity. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2306_01503 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Strategies with minimal norm are optimal for expected utility maximization under high model ambiguity Carassus, Laurence Wiesel, Johannes Optimization and Control Probability Mathematical Finance We investigate an expected utility maximization problem under model uncertainty in a one-period financial market. We capture model uncertainty by replacing the baseline model $\mathbb{P}$ with an adverse choice from a Wasserstein ball of radius $k$ around $\mathbb{P}$ in the space of probability measures and consider the corresponding Wasserstein distributionally robust optimization problem. We show that optimal solutions converge to a strategy with minimal norm when uncertainty is increasingly large, i.e. when the radius $k$ tends to infinity. |
| title | Strategies with minimal norm are optimal for expected utility maximization under high model ambiguity |
| topic | Optimization and Control Probability Mathematical Finance |
| url | https://arxiv.org/abs/2306.01503 |