Properties of a Risk Measure Derived from Ruin Theory

Julien Trufin, Hansjoerg Albrecher and Michel M Denuit
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Julien Trufin: Institut de Statistique, Biostatistique et Sciences Actuarielles (ISBA), Universite Catholique de Louvain, B-1348 Louvain-la-Neuve, Belgium
Hansjoerg Albrecher: Ecole des HEC (Business School), University of Lausanne, Lausanne CH-1015, Switzerland
Michel M Denuit: Institut de Statistique, Biostatistique et Sciences Actuarielles (ISBA), Universite Catholique de Louvain, B-1348 Louvain-la-Neuve, Belgium

The Geneva Risk and Insurance Review, 2011, vol. 36, issue 2, 174-188

Abstract: This paper studies a risk measure inherited from ruin theory and investigates some of its properties. Specifically, we consider a value-at-risk (VaR)-type risk measure defined as the smallest initial capital needed to ensure that the ultimate ruin probability is less than a given level. This VaR-type risk measure turns out to be equivalent to the VaR of the maximal deficit of the ruin process in infinite time. A related Tail-VaR-type risk measure is also discussed.

Date: 2011
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