Risk measures based on weak optimal transport

Michael Kupper, Max Nendel and Alessandro Sgarabottolo
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Michael Kupper: Center for Mathematical Economics, Bielefeld University
Max Nendel: Center for Mathematical Economics, Bielefeld University
Alessandro Sgarabottolo: Center for Mathematical Economics, Bielefeld University

No 734, Center for Mathematical Economics Working Papers from Center for Mathematical Economics, Bielefeld University

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, uncertainty on path spaces, moment constrains, and martingale constraints. In a last step, we show how to use the theoretical results for the numerical computation of worstcase losses in an insurance context and no-arbitrage prices of European contingent claims after quoted maturities in a model-free setting.

Keywords: Risk measure; weak optimal transport; neural network; model uncertainty; martingale optimal transport (search for similar items in EconPapers)
Pages: 24
Date: 2025-08-14
New Economics Papers: this item is included in nep-rmg
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https://pub.uni-bielefeld.de/download/3006160/3006161 First Version, 2023 (application/pdf)

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Persistent link: https://EconPapers.repec.org/RePEc:bie:wpaper:734

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