Optimal payoff under Bregman-Wasserstein divergence constraints

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 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.

Keywords: Portfolio choice, Preferences, Expected Utility, Hoeffding-Fréchet bounds, Bregman Divergence, Wasserstein distance, cost-efficiency