Optimal payoff under Bregman-Wasserstein divergence constraints

Fuente: arXiv
Gespeichert in:
Bibliographische Detailangaben
Hauptverfasser: Pesenti, Silvana M., Vanduffel, Steven, Yang, Yang, Yao, Jing
Format: Preprint
Veröffentlicht: 2024
Schlagworte:
Online-Zugang:
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
_version_ 1866916018847219712
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