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Risk measures based on weak optimal transport

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  • Michael Kupper
  • Max Nendel
  • Alessandro Sgarabottolo

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 worst-case losses in an insurance context and no-arbitrage prices of European contingent claims after quoted maturities in a model-free setting.

Suggested Citation

  • Michael Kupper & Max Nendel & Alessandro Sgarabottolo, 2023. "Risk measures based on weak optimal transport," Papers 2312.05973, arXiv.org.
    • Handle: RePEc:arx:papers:2312.05973
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    References listed on IDEAS

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    Cited by:

    1. Jonas Blessing & Michael Kupper & Alessandro Sgarabottolo, 2024. "Discrete approximation of risk-based prices under volatility uncertainty," Papers 2411.00713, arXiv.org.

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