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Asymptotic consistency of risk functionals

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  • David Wozabal
  • Nancy Wozabal

Abstract

Risk measures are functionals on spaces of random variables designed to quantify financial risk. In this paper, we consider the statistical properties of plug-in estimates for the broad class of coherent, law invariant risk functionals. In particular, we provide several sets of sufficient conditions to establish asymptotic consistency based on a general representation result for this class of functionals. We demonstrate the applicability of our approach by applying it to several well-known examples of risk functionals.

Suggested Citation

  • David Wozabal & Nancy Wozabal, 2009. "Asymptotic consistency of risk functionals," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 21(8), pages 977-990.
    • Handle: RePEc:taf:gnstxx:v:21:y:2009:i:8:p:977-990
    DOI: 10.1080/10485250903060592
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    Cited by:

    1. So Yeon Chun & Alexander Shapiro & Stan Uryasev, 2012. "Conditional Value-at-Risk and Average Value-at-Risk: Estimation and Asymptotics," Operations Research, INFORMS, vol. 60(4), pages 739-756, August.
    2. Henryk Zähle, 2011. "Rates of almost sure convergence of plug-in estimates for distortion risk measures," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 74(2), pages 267-285, September.

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