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Bootstrapping Average Value at Risk of Single and Collective Risks

Author

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  • 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
    1. S. Pitts, 1994. "Nonparametric estimation of compound distributions with applications in insurance," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 46(3), pages 537-555, September.
    2. Acerbi, Carlo, 2002. "Spectral measures of risk: A coherent representation of subjective risk aversion," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1505-1518, July.
    3. Acerbi, Carlo & Tasche, Dirk, 2002. "On the coherence of expected shortfall," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1487-1503, July.
    4. Carlo Acerbi & Dirk Tasche, 2002. "Expected Shortfall: A Natural Coherent Alternative to Value at Risk," Economic Notes, Banca Monte dei Paschi di Siena SpA, vol. 31(2), pages 379-388, July.
    5. Bølviken, Erik & Guillen, Montserrat, 2017. "Risk aggregation in Solvency II through recursive log-normals," Insurance: Mathematics and Economics, Elsevier, vol. 73(C), pages 20-26.
    6. Susanne Emmer & Marie Kratz & Dirk Tasche, 2013. "What is the best risk measure in practice? A comparison of standard measures," Papers 1312.1645, arXiv.org, revised Apr 2015.
    7. Lauer, Alexandra & Zähle, Henryk, 2017. "Bootstrap consistency and bias correction in the nonparametric estimation of risk measures of collective risks," Insurance: Mathematics and Economics, Elsevier, vol. 74(C), pages 99-108.
    8. Bruce Jones & Ričardas Zitikis, 2003. "Empirical Estimation of Risk Measures and Related Quantities," North American Actuarial Journal, Taylor & Francis Journals, vol. 7(4), pages 44-54.
    9. Hideatsu Tsukahara, 2013. "Estimation of Distortion Risk Measures," Journal of Financial Econometrics, Oxford University Press, vol. 12(1), pages 213-235, December.
    10. 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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