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Bootstrapping Average Value at Risk of Single and Collective Risks

Author

Listed:
  • Eric Beutner

    (Department of Quantitative Economics, Maastricht University, 6200 MD Maastricht, The Netherlands)

  • Henryk Zähle

    (Department of Mathematics, Saarland University, 66123 Saarbrücken, Germany)

Abstract

Almost sure bootstrap consistency of the blockwise bootstrap for the Average Value at Risk of single risks is established for strictly stationary β -mixing observations. Moreover, almost sure bootstrap consistency of a multiplier bootstrap for the Average Value at Risk of collective risks is established for independent observations. The main results rely on a new functional delta-method for the almost sure bootstrap of uniformly quasi-Hadamard differentiable statistical functionals, to be presented here. The latter seems to be interesting in its own right.

Suggested Citation

  • Eric Beutner & Henryk Zähle, 2018. "Bootstrapping Average Value at Risk of Single and Collective Risks," Risks, MDPI, vol. 6(3), pages 1-30, September.
    • Handle: RePEc:gam:jrisks:v:6:y:2018:i:3:p:96-:d:169405
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    References listed on IDEAS

    as
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    5. Beutner, Eric & Zähle, Henryk, 2010. "A modified functional delta method and its application to the estimation of risk functionals," Journal of Multivariate Analysis, Elsevier, vol. 101(10), pages 2452-2463, November.
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