Journal of Applied Probability

Central limit theorems for law-invariant coherent risk measures

Denis Belomestny and Volker Krätschmer

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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.

Article information

J. Appl. Probab., Volume 49, Number 1 (2012), 1-21.

First available in Project Euclid: 8 March 2012

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

Law-invariant coherent risk measure canonical plugin estimate functional central limit theorem weak dependence


Belomestny, Denis; Krätschmer, Volker. Central limit theorems for law-invariant coherent risk measures. J. Appl. Probab. 49 (2012), no. 1, 1--21. doi:10.1239/jap/1331216831.

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