Risk measures based on weak optimal transport

Michael Kupper, Max Nendel and Alessandro Sgarabottolo

Quantitative Finance, 2025, vol. 25, issue 2, 163-180

Abstract: In this paper, we study convex risk measures with weak optimal transport penalties. In a first step, we show that these risk measures allow for an explicit representation via a nonlinear transform of the loss function. In a second step, we discuss computational aspects related to the nonlinear transform as well as approximations of the risk measures using, for example, neural networks. Our setup comprises a variety of examples, such as classical optimal transport penalties, parametric families of models, divergence risk measures, uncertainty on path spaces, moment constraints, and martingale constraints. In a last step, we show how to use the theoretical results for the numerical computation of worst-case losses in an insurance context and no-arbitrage prices of European contingent claims after quoted maturities in a model-free setting.

Date: 2025
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DOI: 10.1080/14697688.2024.2403540

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