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A parametric approach to the estimation of convex risk functionals based on Wasserstein distance

Author

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  • Nendel, Max

    (Center for Mathematical Economics, Bielefeld University)

  • Sgarabottolo, Alessandro

    (Center for Mathematical Economics, Bielefeld University)

Abstract

In this paper, we explore a static setting for the assessment of risk in the context of mathematical finance and actuarial science that takes into account model uncertainty in the distribution of a possibly infinite-dimensional risk factor. We study convex risk functionals that incorporate a safety margin with respect to nonparametric uncertainty by penalizing perturbations from a given baseline model using Wasserstein distance. We investigate to which extent this form of probabilistic imprecision can be approximated by restricting to a parametric family of models. The particular form of the parametrization allows to develop numerical methods based on neural networks, which give both the value of the risk functional and the worst-case perturbation of the reference measure. Moreover, we consider additional constraints on the perturbations, namely, mean and martingale constraints. We show that, in both cases, under suitable conditions on the loss function, it is still possible to estimate the risk functional by passing to a parametric family of perturbed models, which again allows for numerical approximations via neural networks.

Suggested Citation

  • Nendel, Max & Sgarabottolo, Alessandro, 2025. "A parametric approach to the estimation of convex risk functionals based on Wasserstein distance," Center for Mathematical Economics Working Papers 724, Center for Mathematical Economics, Bielefeld University.
    • Handle: RePEc:bie:wpaper:724
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    References listed on IDEAS

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    1. Daniel Bartl & Samuel Drapeau & Jan Obloj & Johannes Wiesel, 2020. "Sensitivity analysis of Wasserstein distributionally robust optimization problems," Papers 2006.12022, arXiv.org, revised Nov 2021.
    2. Stephan Eckstein & Michael Kupper & Mathias Pohl, 2020. "Robust risk aggregation with neural networks," Mathematical Finance, Wiley Blackwell, vol. 30(4), pages 1229-1272, October.
    3. Stephan Eckstein & Michael Kupper & Mathias Pohl, 2018. "Robust risk aggregation with neural networks," Papers 1811.00304, arXiv.org, revised May 2020.
    4. Mathias Beiglbock & Pierre Henry-Labord`ere & Friedrich Penkner, 2011. "Model-independent Bounds for Option Prices: A Mass Transport Approach," Papers 1106.5929, arXiv.org, revised Feb 2013.
    5. David Wozabal, 2012. "A framework for optimization under ambiguity," Annals of Operations Research, Springer, vol. 193(1), pages 21-47, March.
    6. Daniel Bartl & Samuel Drapeau & Ludovic Tangpi, 2020. "Computational aspects of robust optimized certainty equivalents and option pricing," Mathematical Finance, Wiley Blackwell, vol. 30(1), pages 287-309, January.
    7. Mathias Beiglböck & Pierre Henry-Labordère & Friedrich Penkner, 2013. "Model-independent bounds for option prices—a mass transport approach," Finance and Stochastics, Springer, vol. 17(3), pages 477-501, July.
    8. Rama Cont, 2006. "Model Uncertainty And Its Impact On The Pricing Of Derivative Instruments," Mathematical Finance, Wiley Blackwell, vol. 16(3), pages 519-547, July.
    9. Philippe Artzner & Freddy Delbaen & Jean‐Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228, July.
    10. Georg Pflug & David Wozabal, 2007. "Ambiguity in portfolio selection," Quantitative Finance, Taylor & Francis Journals, vol. 7(4), pages 435-442.
    11. Rama Cont, 2006. "Model uncertainty and its impact on the pricing of derivative instruments," Post-Print halshs-00002695, HAL.
    12. Fuhrmann, Sven & Kupper, Michael & Nendel, Max, 2021. "Wasserstein Perturbations of Markovian Transition Semigroups," Center for Mathematical Economics Working Papers 649, Center for Mathematical Economics, Bielefeld University.
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