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Technical Note—The Joint Impact of F -Divergences and Reference Models on the Contents of Uncertainty Sets

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  • Thomas Kruse

    (Department of Mathematics, University of Duisburg-Essen, D-45127 Essen, Germany;)

  • Judith C. Schneider

    (Finance Center Münster, University of Münster, D-48143 Münster, Germany;)

  • Nikolaus Schweizer

    (Department of Econometrics and Operations Research, Tilburg University, NL-5000 LE Tilburg, Netherlands)

Abstract

In the presence of model risk, it is well established to replace classical expected values with worst-case expectations over all models within a fixed radius from a given reference model. This is the “robustness” approach. For the class of F -divergences, we provide a careful assessment of how the interplay between reference model and divergence measure shapes the contents of uncertainty sets. We show that the classical divergences, relative entropy and polynomial divergences, are inadequate for reference models that are moderately heavy-tailed, such as lognormal models. Worst cases either are infinitely pessimistic or rule out the possibility of fat-tailed “power law” models as plausible alternatives. Moreover, we rule out the existence of a single F -divergence, which is appropriate regardless of the reference model. Thus, the reference model should not be neglected when settling on any particular divergence measure in the robustness approach.

Suggested Citation

  • Thomas Kruse & Judith C. Schneider & Nikolaus Schweizer, 2019. "Technical Note—The Joint Impact of F -Divergences and Reference Models on the Contents of Uncertainty Sets," Operations Research, INFORMS, vol. 67(2), pages 428-435, March.
    • Handle: RePEc:inm:oropre:v:67:y:2019:i:2:p:428-435
    DOI: 10.1287/opre.2018.1807
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    References listed on IDEAS

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    1. 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.
    2. Dimitris Bertsimas & Melvyn Sim, 2004. "The Price of Robustness," Operations Research, INFORMS, vol. 52(1), pages 35-53, February.
    3. R. Cont, 2001. "Empirical properties of asset returns: stylized facts and statistical issues," Quantitative Finance, Taylor & Francis Journals, vol. 1(2), pages 223-236.
    4. Yuhong Xu, 2014. "Robust valuation and risk measurement under model uncertainty," Papers 1407.8024, arXiv.org.
    5. 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.
    6. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
    7. Thomas Breuer & Imre Csiszár, 2016. "Measuring Distribution Model Risk," Mathematical Finance, Wiley Blackwell, vol. 26(2), pages 395-411, April.
    8. 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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