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Properties of risk measures derived from ruin theory

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Trufin, Julien [UCL] Albrecher, Hansjoerg [Université de Lausanne, Suisse] Denuit, Michel [UCL]

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.

Document type Article de périodique (Journal article) – Article de recherche
Publication date 2011
Language Anglais
Journal information "The Geneva Risk and Insurance Review" - Vol. 36, p. 174-188 (2011)
Peer reviewed yes
Publisher Palgrave Macmillan ((United States) New York)
issn 1554-964X
e-issn 1554-9658
Publication status Publié
Affiliations UCL - SSH/LIDAM/ISBA - Institut de Statistique, Biostatistique et Sciences Actuarielles
Université de Lausanne, Suisse - Département Sciences actuarielles
Links
  1. Asmussen Søren, Ruin Probabilities, ISBN:9789810222932, 10.1142/2779
  2. Cheridito Patrick, Delbaen Freddy, Kupper Michael, Coherent and convex monetary risk measures for unbounded càdlàg processes, 10.1007/s00780-006-0017-1
  3. Denuit M., Dhaene J., Goovaerts M., Kaas R., Actuarial Theory for Dependent Risks : Measures, Orders and Models, ISBN:9780470016459, 10.1002/0470016450
  4. Dhaene Jan, Goovaerts Mark J., Kaas Rob, Economic Capital Allocation Derived from Risk Measures, 10.1080/10920277.2003.10596084
  5. Embrechts, P., Kaufmann, R. and Samorodnitsky, G. (2004) ‘Ruin theory revisited: Stochastic models for operational risk’, in C. Bernadell et al. (ed) Risk Management for Central Bank Foreign Reserves, Frankfurt: European Central Bank, pp. 243–261.
  6. Embrechts Paul, Puccetti Giovanni, Aggregating risk capital, with an application to operational risk, 10.1007/s10713-006-0556-6
  7. Geman H., Learning about Risk: Some Lessons from Insurance, 10.1023/a:1009835429630
  8. Heilmann Wolf-Rüdiger, Schröter Klaus J., Orderings of risks and their actuarial applications, Stochastic orders and decision under risk (1991) ISBN:0940600269 p.157-173, 10.1214/lnms/1215459855
  9. Huang Hung-Hsi, Optimal insurance contract under a value-at-risk constraint, 10.1007/s10713-006-0557-5
  10. Kaas Rob, Goovaerts Marc, Dhaene Jan, Denuit Michel, Modern Actuarial Risk Theory, ISBN:9783540709923, 10.1007/978-3-540-70998-5
  11. Lefèvre, C. and Utev, S. (2001) ‘Comparison of individual risk models’, Insurance: Mathematics and Economics 28: 21–30.
  12. Luciano Elisa, Kast Robert, A Value at Risk Approach to Background Risk, 10.1023/a:1014303013248
  13. Michel, R. (1987) ‘A partial ordering of claim amount distributions and its relation to ruin probabilities in the Poisson model’, Bulletin of the Swiss Association of Actuaries 1987: 75–80.
  14. Pflug Georg Ch, Römisch Werner, Modeling, Measuring and Managing Risk, ISBN:9789812707406, 10.1142/6478
  15. Stochastic Orders, ISBN:9780387329154, 10.1007/978-0-387-34675-5
Bibliographic reference Trufin, Julien ; Albrecher, Hansjoerg ; Denuit, Michel. Properties of risk measures derived from ruin theory. In: The Geneva Risk and Insurance Review, Vol. 36, p. 174-188 (2011)
Permanent URL http://hdl.handle.net/2078.1/93546