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A Toolkit for Robust Risk Assessment Using F -Divergences

Author

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  • Thomas Kruse

    (Institute of Mathematics, Justus Liebig University, 35392 Giessen, Germany)

  • Judith C. Schneider

    (Chair of Finance, Leuphana University, 21335 Lüneburg, Germany; Finance Center Münster, University of Münster, 48143 Münster, Germany)

  • Nikolaus Schweizer

    (Department of Econometrics and Operations Research, Tilburg University, 5037AB Tilburg, Netherlands)

Abstract

This paper assembles a toolkit for the assessment of model risk when model uncertainty sets are defined in terms of an F -divergence ball around a reference model. We propose a new family of F -divergences that are easy to implement and flexible enough to imply convincing uncertainty sets for broad classes of reference models. We use our theoretical results to construct concrete examples of divergences that allow for significant amounts of uncertainty about lognormal or heavy-tailed Weibull reference models without implying that the worst case is necessarily infinitely bad. We implement our tools in an open-source software package and apply them to three risk management problems from operations management, insurance, and finance.

Suggested Citation

  • Thomas Kruse & Judith C. Schneider & Nikolaus Schweizer, 2021. "A Toolkit for Robust Risk Assessment Using F -Divergences," Management Science, INFORMS, vol. 67(10), pages 6529-6552, October.
    • Handle: RePEc:inm:ormnsc:v:67:y:2021:i:10:p:6529-6552
    DOI: 10.1287/mnsc.2020.3822
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    References listed on IDEAS

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    1. Dimitris Bertsimas & Melvyn Sim, 2004. "The Price of Robustness," Operations Research, INFORMS, vol. 52(1), pages 35-53, February.
    2. Yuhong Xu, 2014. "Robust valuation and risk measurement under model uncertainty," Papers 1407.8024, arXiv.org.
    3. Schneider, Judith C. & Schweizer, Nikolaus, 2015. "Robust measurement of (heavy-tailed) risks: Theory and implementation," Journal of Economic Dynamics and Control, Elsevier, vol. 61(C), pages 183-203.
    4. A. Ahmadi-Javid, 2012. "Entropic Value-at-Risk: A New Coherent Risk Measure," Journal of Optimization Theory and Applications, Springer, vol. 155(3), pages 1105-1123, December.
    5. Henry Lam, 2016. "Robust Sensitivity Analysis for Stochastic Systems," Mathematics of Operations Research, INFORMS, vol. 41(4), pages 1248-1275, November.
    6. Thomas Breuer & Imre Csiszár, 2016. "Measuring Distribution Model Risk," Mathematical Finance, Wiley Blackwell, vol. 26(2), pages 395-411, April.
    7. Kostas Bimpikis & Mihalis G. Markakis, 2016. "Inventory Pooling Under Heavy-Tailed Demand," Management Science, INFORMS, vol. 62(6), pages 1800-1813, June.
    8. Aharon Ben-Tal & Dick den Hertog & Anja De Waegenaere & Bertrand Melenberg & Gijs Rennen, 2013. "Robust Solutions of Optimization Problems Affected by Uncertain Probabilities," Management Science, INFORMS, vol. 59(2), pages 341-357, April.
    9. Paul Glasserman & Xingbo Xu, 2014. "Robust risk measurement and model risk," Quantitative Finance, Taylor & Francis Journals, vol. 14(1), pages 29-58, January.
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    Citations

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    Cited by:

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