Additivity properties for Value-at-Risk under Archimedean dependence and heavy-tailedness

Insurance: Mathematics and Economics

Volumn 44, Issue 2, 2009, Pages 164-169

  Embrechts, Paul ^a   Nešlehová, Johanna ^a   Wüthrich, Mario V ^a  

^a ETH ZURICH   (Switzerland)

Author keywords

Aggregation; Archimedean copula; Dependence structure; Subadditivity; Value at Risk

Indexed keywords

EID: 63449119587     PISSN: 01676687     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.insmatheco.2008.08.001     Document Type: Article

References (29)

1. Alink S., Löwe M., and Wüthrich M.V. Diversification of aggregate dependent risks. Insurance Mathematics & Economics 35 (2004) 77-95
2. Artzner P., Delbaen F., Eber J.M., and Heath D. Coherent risk measures. Mathematical Finance 9 (1999) 203-228
3. Barbe P., Fougères A.L., and Genest C. On the tail behavior of sums of dependent risks. ASTIN Bulletin 36 2 (2006) 361-374
4. Böcker, K., Klüppelberg, C., 2006. Multivariate models for operational risk. TU Munich. Preprint
5. Daníelsson, J., Jorgensen, B.N., Samorodnitsky, G., Sarma, M., de Vries, C.G., 2005. Subadditivity re-examined: The case for value-at-risk. London School of Economics. Preprint
6. Degen M., Embrechts P., and Lambrigger D. The quantitative modeling of operational risk: Between g-and-h and EVT. ASTIN Bulletin 37 2 (2007) 265-291
7. Dhaene J., Laeven R., Vanduffel S., Darkiewicz C., and Goovaerts M. Can a coherent risk measure be too subadditive?. Journal of Risk and Insurance 75 2 (2008) 365-386
8. Dutta, K., Perry, J., 2007. A tale of tails: An empirical analysis of loss distribution models for estimating operational risk capital. Working Paper. Federal Reserve Bank of Boston, No. 06-13
9. Embrechts P., Klüppelberg C., and Mikosch T. Modelling Extremal Events for Insurance and Finance (1997), Springer, Berlin
10. de Fontnouvelle P., Rosengren E., and Jordan J. Implications of alternative operational risk modeling techniques. In: Carey M., and Stulz R. (Eds). The Risks of Financial Institutions (2006), NBER/University of Chicago Press 475-511
11. Fortuin C.M., Kasteleyn P.W., and Ginibre J. Correlation inequalities on some partially ordered sets. Communications in Mathematical Physics 22 (1971) 89-103
12. Heyde, C.C., Kou, S.G., Peng, X.H., 2006. What is a good risk measure: Bridging the gaps between data, coherent risk measures, and insurance risk measures. Columbia University. Preprint
13. Joe H. Multivariate Models and Dependence Concepts (1997), Chapman and Hall, London
14. Kemperman J.H.B. On the FKG-inequalities for measures on a partially ordered space. Koninklijke Nederlandse Akademie van Wetenschappen. Proceedings. Series A 80 (1977) 313-331
15. Kimberling C. A probabilistic interpretation of complete monotonicity. Aequationes Mathematica 10 (1974) 152-164
16. Kotz S., and Nadarajah S. Extreme Value Distributions: Theory and Applications (2000), Imperial College Press, London
17. McNeil A.J., Frey R., and Embrechts P. Quantitative Risk Management: Concepts, Techniques and Tools (2005), Princeton University Press, Princeton
18. 1-norm symmetric distributions, Annals of Statistics (in press)
19. Mikosch T., and Nagaev A. Rates in approximations to ruin probabilities for heavy-tailed distributions. Extremes 4/1 (2001) 67-78
20. Moscadelli, M., 2004. The modelling of operational risk: Experience with the analysis of the data collected by the Basel Committee. Technical Report 517. Banca d'Italia
21. Müller A. Stop-loss order for portfolios of dependent risks. Insurance Mathematics & Economics 21 (1997) 219-223
22. Nelsen R.B. An Introduction to Copulas. second ed (2006), Springer, New York
23. Nešlehová J., Embrechts P., and Chavez-Demoulin V. Infinite mean models and the LDA for operational risk. Journal of Operational Risk 1/1 (2006) 3-25
24. Newman C.M. Topics in Disordered Systems. Lectures in Mathematics, ETH Zürich (1997), Birkhäuser Verlag, Basel
25. Resnick S.I. Extreme Values, Regular Variation and Point Processes (1987), Springer, New York
26. Resnick S.I. The extremal dependence measure and asymptotic independence. Stochastic Models 20/2 (2004) 205-227
27. Rootzén H., and Klüppelberg C. A single number can't hedge against economic catastrophes. Ambio-Royal Swedish Academy of Sciences 28 (1999) 550-555
28. Wei G., and Hu T. Supermodular dependence ordering on a class of multivariate copulas. Statistics & Probability Letters 57 (2002) 375-385
29. Wüthrich M.V. Asymptotic Value-at-Risk estimates for sums of dependent random variables. ASTIN Bulletin 33 1 (2003) 75-92