Optimal payoff under Bregman-Wasserstein divergence constraints
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866916018847219712 |
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| author | Pesenti, Silvana M. Vanduffel, Steven Yang, Yang Yao, Jing |
| author_facet | Pesenti, Silvana M. Vanduffel, Steven Yang, Yang Yao, Jing |
| contents | We study optimal payoff choice for an expected utility maximizer under the constraint that their payoff is not allowed to deviate ``too much'' from a given benchmark. We solve this problem when the deviation is assessed via a Bregman-Wasserstein (BW) divergence, generated by a convex function $ϕ$. Unlike the Wasserstein distance (i.e., when $ϕ(x)=x^2$) the inherent asymmetry of the BW divergence makes it possible to penalize positive deviations different than negative ones. As a main contribution, we provide the optimal payoff in this setting. Numerical examples illustrate that the choice of $ϕ$ allow to better align the payoff choice with the objectives of investors. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_18397 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Optimal payoff under Bregman-Wasserstein divergence constraints Pesenti, Silvana M. Vanduffel, Steven Yang, Yang Yao, Jing Portfolio Management Mathematical Finance Risk Management We study optimal payoff choice for an expected utility maximizer under the constraint that their payoff is not allowed to deviate ``too much'' from a given benchmark. We solve this problem when the deviation is assessed via a Bregman-Wasserstein (BW) divergence, generated by a convex function $ϕ$. Unlike the Wasserstein distance (i.e., when $ϕ(x)=x^2$) the inherent asymmetry of the BW divergence makes it possible to penalize positive deviations different than negative ones. As a main contribution, we provide the optimal payoff in this setting. Numerical examples illustrate that the choice of $ϕ$ allow to better align the payoff choice with the objectives of investors. |
| title | Optimal payoff under Bregman-Wasserstein divergence constraints |
| topic | Portfolio Management Mathematical Finance Risk Management |
| url | https://arxiv.org/abs/2411.18397 |