Optimal payoff under Bregman-Wasserstein divergence constraints

TL;DR

This paper derives the optimal payoff for an expected utility maximizer constrained by a Bregman-Wasserstein divergence, allowing asymmetric deviation penalties to better match investor objectives.

Contribution

It provides the explicit form of the optimal payoff under Bregman-Wasserstein divergence constraints, extending previous Wasserstein-based models.

Findings

Optimal payoff formula under BW divergence derived

Asymmetry in divergence allows tailored deviation penalties

Numerical examples show improved alignment with investor goals

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.