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Risk Measures and Multivariate Extensions of Breiman's Theorem

Part of: Mathematical economics Applications

Published online by Cambridge University Press:  04 February 2016

Anne-Laure Fougeres  and
Cecile Mercadier
Anne-Laure Fougeres*
Affiliation:
Université Lyon 1
Cecile Mercadier*
Affiliation:
Université Lyon 1
*
∗ Postal address: Université de Lyon, CNRS UMR 5208, Université Lyon 1, Institut Camille Jordan, 43 Boulevard du 11 Novembre 1918, F-69622 Villeurbanne cedex, France.
∗ Postal address: Université de Lyon, CNRS UMR 5208, Université Lyon 1, Institut Camille Jordan, 43 Boulevard du 11 Novembre 1918, F-69622 Villeurbanne cedex, France.
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Abstract

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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.

Keywords

Discrete-time modelruin probabilityvalue at riskmultivariate regular variationdependent risk

MSC classification

Primary: 91B30: Risk theory, insurance
Secondary: 62P05: Applications to actuarial sciences and financial mathematics
Type
Research Article
Information
Journal of Applied Probability , Volume 49 , Issue 2 , June 2012 , pp. 364 - 384
Copyright
© Applied Probability Trust 

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