Bootstrapping average value at risk of single and collective risks

Eric Beutner; Henryk Zähle

doi:10.3390/risks6030096

Bootstrapping average value at risk of single and collective risks

Eric Beutner, Henryk Zähle^*

^*Corresponding author for this work

Research output: Contribution to Journal › Article › Academic › peer-review

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.

Original language	English
Article number	96
Journal	Risks
Volume	6
Issue number	3
DOIs	https://doi.org/10.3390/risks6030096
Publication status	Published - 1 Sept 2018
Externally published	Yes

Keywords

Average value at risk
Blockwise bootstrap
Chain rule
Compound distribution
Functional delta-method
Multiplier bootstrap
Nonparametric estimation
Uniform quasi-hadamard differentiability

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10.3390/risks6030096

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AU - Zähle, Henryk

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N2 - 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.

AB - 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.

KW - Average value at risk

KW - Blockwise bootstrap

KW - Chain rule

KW - Compound distribution

KW - Functional delta-method

KW - Multiplier bootstrap

KW - Nonparametric estimation

KW - Uniform quasi-hadamard differentiability

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VL - 6

JO - Risks

JF - Risks

IS - 3

M1 - 96

ER -

Bootstrapping average value at risk of single and collective risks

Abstract

Keywords

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