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Risk measures based on weak optimal transport

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  • Kupper, Michael

    (Center for Mathematical Economics, Bielefeld University)

  • Nendel, Max

    (Center for Mathematical Economics, Bielefeld University)

  • Sgarabottolo, Alessandro

    (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.

Suggested Citation

  • Kupper, Michael & Nendel, Max & Sgarabottolo, Alessandro, 2025. "Risk measures based on weak optimal transport," Center for Mathematical Economics Working Papers 734, Center for Mathematical Economics, Bielefeld University.
    • Handle: RePEc:bie:wpaper:734
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    File URL: https://pub.uni-bielefeld.de/download/3006160/3006161
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