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What's in a ball? Constructing and characterizing uncertainty sets

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  • Thomas Kruse
  • Judith C. Schneider
  • Nikolaus Schweizer

Abstract

In the presence of model risk, it is well-established to replace classical expected values by worst-case expectations over all models within a fixed radius from a given reference model. This is the "robustness" approach. We show that previous methods for measuring this radius, e.g. relative entropy or polynomial divergences, are inadequate for reference models which are moderately heavy-tailed such as lognormal models. Worst cases are either infinitely pessimistic, or they rule out the possibility of fat-tailed "power law" models as plausible alternatives. We introduce a new family of divergence measures which captures intermediate levels of pessimism.

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  • Thomas Kruse & Judith C. Schneider & Nikolaus Schweizer, 2015. "What's in a ball? Constructing and characterizing uncertainty sets," Papers 1510.01675, arXiv.org.
    • Handle: RePEc:arx:papers:1510.01675
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    References listed on IDEAS

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    1. Hansen, Lars Peter & Sargent, Thomas J., 2011. "Robustness and ambiguity in continuous time," Journal of Economic Theory, Elsevier, vol. 146(3), pages 1195-1223, May.
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    3. Yuhong Xu, 2014. "Robust valuation and risk measurement under model uncertainty," Papers 1407.8024, arXiv.org.
    4. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
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    7. Thomas Breuer & Imre Csiszar, 2013. "Measuring Model Risk," Papers 1301.4832, arXiv.org.
    8. 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.
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