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June 2012 Risk measures and multivariate extensions of Breiman's theorem
Anne-Laure Fougeres, Cecile Mercadier
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J. Appl. Probab. 49(2): 364-384 (June 2012). DOI: 10.1239/jap/1339878792

Abstract

The modeling of insurance risks has received an increasing amount of attention because of solvency capital requirements. The ruin probability has become a standard risk measure to assess regulatory capital. In this paper we focus on discrete-time models for the finite time horizon. Several results are available in the literature to calibrate the ruin probability by means of the sum of the tail probabilities of individual claim amounts. The aim of this work is to obtain asymptotics for such probabilities under multivariate regular variation and, more precisely, to derive them from extensions of Breiman's theorem. We thus present new situations where the ruin probability admits computable equivalents. We also derive asymptotics for the value at risk.

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Anne-Laure Fougeres. Cecile Mercadier. "Risk measures and multivariate extensions of Breiman's theorem." J. Appl. Probab. 49 (2) 364 - 384, June 2012. https://doi.org/10.1239/jap/1339878792

Information

Published: June 2012
First available in Project Euclid: 16 June 2012

zbMATH: 1246.91060
MathSciNet: MR2977801
Digital Object Identifier: 10.1239/jap/1339878792

Subjects:
Primary: 91B30
Secondary: 62P05

Keywords: dependent risk , Discrete-time model , multivariate regular variation , ruin probability , value at risk

Rights: Copyright © 2012 Applied Probability Trust

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Vol.49 • No. 2 • June 2012
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