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Central Limit Theorems for Law-Invariant Coherent Risk Measures

Part of: Limit theorems Parametric inference Nonparametric inference Mathematical economics

Published online by Cambridge University Press:  04 February 2016

Denis Belomestny  and
Volker Krätschmer
Denis Belomestny*
Affiliation:
University of Duisburg-Essen
Volker Krätschmer*
Affiliation:
University of Duisburg-Essen
*
∗ Postal address: Faculty of Mathematics, University of Duisburg-Essen, D-47057 Duisburg, Germany.
∗ Postal address: Faculty of Mathematics, University of Duisburg-Essen, D-47057 Duisburg, Germany.
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Abstract

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In this paper we study the asymptotic properties of the canonical plugin estimates for law-invariant coherent risk measures. Under rather mild conditions not relying on the explicit representation of the risk measure under consideration, we first prove a central limit theorem for independent and identically distributed data, and then extend it to the case of weakly dependent data. Finally, a number of illustrating examples is presented.

Keywords

Law-invariant coherent risk measurecanonical plugin estimatefunctional central limit theoremweak dependence

MSC classification

Primary: 60F05: Central limit and other weak theorems 62F12: Asymptotic properties of estimators
Secondary: 60F17: Functional limit theorems; invariance principles 62G30: Order statistics; empirical distribution functions 91B30: Risk theory, insurance
Type
Research Article
Information
Journal of Applied Probability , Volume 49 , Issue 1 , March 2012 , pp. 1 - 21
Copyright
© Applied Probability Trust 

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