Bootstrapping Average Value at Risk of Single and Collective Risks

Eric Beutner; Henryk Zaehle

doi:10.3390/risks6030096

Bootstrapping Average Value at Risk of Single and Collective Risks

Eric Beutner, Henryk Zaehle^*

^*Corresponding author for this work

QE Math. Economics & Game Theory

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
Number of pages	30
Journal	Risks
Volume	6
Issue number	3
DOIs	https://doi.org/10.3390/risks6030096
Publication status	Published - Sept 2018

Keywords

Average Value at Risk
compound distribution
nonparametric estimation
multiplier bootstrap
blockwise bootstrap
functional delta-method
uniform quasi-Hadamard differentiability
chain rule
NONSEPARABLE METRIC-SPACES
FUNCTIONAL DELTA-METHOD
EMPIRICAL PROCESSES
STATIONARY-SEQUENCES
BLOCKWISE BOOTSTRAP
ORDER-STATISTICS
NONPARAMETRIC-ESTIMATION
INFERENCE

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title = "Bootstrapping Average Value at Risk of Single and Collective Risks",

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, NONSEPARABLE METRIC-SPACES, FUNCTIONAL DELTA-METHOD, EMPIRICAL PROCESSES, STATIONARY-SEQUENCES, BLOCKWISE BOOTSTRAP, ORDER-STATISTICS, NONPARAMETRIC-ESTIMATION, INFERENCE",

author = "Eric Beutner and Henryk Zaehle",

note = "data source: No data were used.",

year = "2018",

month = sep,

doi = "10.3390/risks6030096",

language = "English",

volume = "6",

journal = "Risks",

issn = "2227-9091",

publisher = "Multidisciplinary Digital Publishing Institute (MDPI)",

number = "3",

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TY - JOUR

T1 - Bootstrapping Average Value at Risk of Single and Collective Risks

AU - Beutner, Eric

AU - Zaehle, Henryk

N1 - data source: No data were used.

PY - 2018/9

Y1 - 2018/9

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 - compound distribution

KW - nonparametric estimation

KW - multiplier bootstrap

KW - blockwise bootstrap

KW - functional delta-method

KW - uniform quasi-Hadamard differentiability

KW - chain rule

KW - NONSEPARABLE METRIC-SPACES

KW - FUNCTIONAL DELTA-METHOD

KW - EMPIRICAL PROCESSES

KW - STATIONARY-SEQUENCES

KW - BLOCKWISE BOOTSTRAP

KW - ORDER-STATISTICS

KW - NONPARAMETRIC-ESTIMATION

KW - INFERENCE

U2 - 10.3390/risks6030096

DO - 10.3390/risks6030096

M3 - Article

SN - 2227-9091

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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