Publication:
Large deviations built on max-stability

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2021-bernoulli-Vol27_No2-1001-1027.pdf(259.31 KB)
Date
2021-05
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Authors
Kupper, Michael
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Publisher
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EstadĂ­stica e InvestigaciĂłn Operativa
DOI
https://doi.org/10.3150/20-BEJ1263
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info:eu-repo/semantics/article
Description
© 2021, International Statistical Institute/Bernoulli Society for Mathematical Statistics and Probability. This document is the Published version of a Published Work that appeared in final form in Bernoulli. To access the final edited and published work see https://doi.org/10.3150/20-BEJ1263
Abstract
In this paper, we show that the basic results in large deviations theory hold for general monetary risk measures, which satisfy the crucial property of max-stability. A max-stable monetary risk measure fulfills a lattice homomorphism property, and satisfies under a suitable tightness condition the Laplace Principle (LP), that is, admits a dual representation with affine convex conjugate. By replacing asymptotic concentration of probability by concentration of risk, we formulate a Large Deviation Principle (LDP) for max-stable monetary risk measures, and show its equivalence to the LP. In particular, the special case of the asymptotic entropic risk measure corresponds to the classical Varadhan–Bryc equivalence between the LDP and LP. The main results are illustrated by the asymptotic shortfall risk measure.
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Large deviations , Max-stable monetary risk measures , Large Deviation Principle , Laplace Principle , Concentration function , Asymptotic shortfall risk
Citation
Bernoulli 27(2), 2021, 1001–1027
URI
http://hdl.handle.net/10201/149309
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