Asymptotic consistency of risk functionals

David Wozabal; Nancy Wozabal

doi:10.1080/10485250903060592

Asymptotic consistency of risk functionals

David Wozabal
, Nancy Wozabal

Research output: Contribution to journal › Article › peer-review

5 Scopus citations

Abstract

Risk measures are functionals on spaces of random variables designed to quantify financial risk. In this paper, we consider the statistical properties of plug-in estimates for the broad class of coherent, law invariant risk functionals. In particular, we provide several sets of sufficient conditions to establish asymptotic consistency based on a general representation result for this class of functionals. We demonstrate the applicability of our approach by applying it to several well-known examples of risk functionals.

Original language	English
Pages (from-to)	977-990
Number of pages	14
Journal	Journal of Nonparametric Statistics
Volume	21
Issue number	8
DOIs	https://doi.org/10.1080/10485250903060592
State	Published - Nov 2009
Externally published	Yes

Keywords

Asymptotic consistency
Coherent risk functionals
L-statistics
Law of large numbers
Law-invariance

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10.1080/10485250903060592

Cite this

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AB - Risk measures are functionals on spaces of random variables designed to quantify financial risk. In this paper, we consider the statistical properties of plug-in estimates for the broad class of coherent, law invariant risk functionals. In particular, we provide several sets of sufficient conditions to establish asymptotic consistency based on a general representation result for this class of functionals. We demonstrate the applicability of our approach by applying it to several well-known examples of risk functionals.

KW - Asymptotic consistency

KW - Coherent risk functionals

KW - L-statistics

KW - Law of large numbers

KW - Law-invariance

UR - https://www.scopus.com/pages/publications/77649125268

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DO - 10.1080/10485250903060592

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JO - Journal of Nonparametric Statistics

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ER -

Asymptotic consistency of risk functionals

Abstract

Keywords

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