Optimal payoff under Bregman-Wasserstein divergence constraints

2024/11/27 by Pesenti, Silvana M., Vanduffel, Steven, Yang, Yang +1 · 4 citations
#FOS: Economics and business #Mathematical Finance (q-fin.MF) #Portfolio Management (q-fin.PM) #Risk Management (q-fin.RM)

paper · doi:10.48550/arxiv.2411.18397

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)=x²) 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.

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