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Risks 2018, 6(3), 96; https://doi.org/10.3390/risks6030096

Bootstrapping Average Value at Risk of Single and Collective Risks

1
Department of Quantitative Economics, Maastricht University, 6200 MD Maastricht, The Netherlands
2
Department of Mathematics, Saarland University, 66123 Saarbrücken, Germany
*
Author to whom correspondence should be addressed.
Received: 1 August 2018 / Revised: 27 August 2018 / Accepted: 7 September 2018 / Published: 12 September 2018
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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. View Full-Text
Keywords: Average Value at Risk; compound distribution; nonparametric estimation; multiplier bootstrap; blockwise bootstrap; functional delta-method; uniform quasi-Hadamard differentiability; chain rule Average Value at Risk; compound distribution; nonparametric estimation; multiplier bootstrap; blockwise bootstrap; functional delta-method; uniform quasi-Hadamard differentiability; chain rule
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).
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Beutner, E.; Zähle, H. Bootstrapping Average Value at Risk of Single and Collective Risks. Risks 2018, 6, 96.

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