Bootstrapping Average Value at Risk of Single and Collective Risks

Eric Beutner and Henryk Zähle
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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

Risks, 2018, vol. 6, issue 3, 1-30

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.

Keywords: Average Value at Risk; compound distribution; nonparametric estimation; multiplier bootstrap; blockwise bootstrap; functional delta-method; uniform quasi-Hadamard differentiability; chain rule (search for similar items in EconPapers)
JEL-codes: C G0 G1 G2 G3 K2 M2 M4 (search for similar items in EconPapers)
Date: 2018
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