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arXiv · 2411.18397

Optimal payoff under Bregman-Wasserstein divergence constraints

Silvana M. Pesenti·Steven Vanduffel·Yang Yang·Jing Yao
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Abstract

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 $\phi$. Unlike the Wasserstein distance (i.e., when $\phi(x)=x^2$) 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 $\phi$ allow to better align the payoff choice with the objectives of investors.

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Silvana M. Pesenti, Steven Vanduffel, Yang Yang, Jing Yao. 2024-11-27. Optimal payoff under Bregman-Wasserstein divergence constraints. https://arxiv.org/abs/2411.18397

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