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Measuring Model Risk

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  • Thomas Breuer
  • Imre Csiszar
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    Abstract

    We propose to interpret distribution model risk as sensitivity of expected loss to changes in the risk factor distribution, and to measure the distribution model risk of a portfolio by the maximum expected loss over a set of plausible distributions defined in terms of some divergence from an estimated distribution. The divergence may be relative entropy, a Bregman distance, or an $f$-divergence. We give formulas for the calculation of distribution model risk and explicitly determine the worst case distribution from the set of plausible distributions. We also give formulas for the evaluation of divergence preferences describing ambiguity averse decision makers.

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    File URL: http://arxiv.org/pdf/1301.4832
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    Bibliographic Info

    Paper provided by arXiv.org in its series Papers with number 1301.4832.

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    Date of creation: Jan 2013
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    Handle: RePEc:arx:papers:1301.4832

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    1. Thomas J. Sargent & LarsPeter Hansen, 2001. "Robust Control and Model Uncertainty," American Economic Review, American Economic Association, American Economic Association, vol. 91(2), pages 60-66, May.
    2. Barillas, Francisco & Hansen, Lars Peter & Sargent, Thomas J., 2009. "Doubts or variability?," Journal of Economic Theory, Elsevier, Elsevier, vol. 144(6), pages 2388-2418, November.
    3. Kerkhof, Jeroen & Melenberg, Bertrand & Schumacher, Hans, 2010. "Model risk and capital reserves," Journal of Banking & Finance, Elsevier, Elsevier, vol. 34(1), pages 267-279, January.
    4. Hansen, Lars Peter & Sargent, Thomas J., 2007. "Recursive robust estimation and control without commitment," Journal of Economic Theory, Elsevier, Elsevier, vol. 136(1), pages 1-27, September.
    5. Ramon Casadesus-Masanell & Peter Klibanoff & Emre Ozdenoren, 1998. "Maximum Expected Utility over Savage Acts with a Set of Priors," Discussion Papers, Northwestern University, Center for Mathematical Studies in Economics and Management Science 1218, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    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. Rama Cont, 2006. "Model uncertainty and its impact on the pricing of derivative instruments," Post-Print halshs-00002695, HAL.
    8. Philippe Artzner & Freddy Delbaen & Jean-Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, Wiley Blackwell, vol. 9(3), pages 203-228.
    9. Fabio Maccheroni & Massimo Marinacci & Aldo Rustichini, 2006. "Ambiguity Aversion, Robustness, and the Variational Representation of Preferences," Econometrica, Econometric Society, Econometric Society, vol. 74(6), pages 1447-1498, November.
    10. Golan, Amos & Judge, George G. & Miller, Douglas, 1996. "Maximum Entropy Econometrics," Staff General Research Papers 1488, Iowa State University, Department of Economics.
    11. Marco Avellaneda & Antonio ParAS, 1996. "Managing the volatility risk of portfolios of derivative securities: the Lagrangian uncertain volatility model," Applied Mathematical Finance, Taylor & Francis Journals, Taylor & Francis Journals, vol. 3(1), pages 21-52.
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