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Worst case risk measurement: Back to the future?

Listed author(s):
  • Goovaerts, Marc J.
  • Kaas, Rob
  • Laeven, Roger J.A.

This paper studies the problem of finding best-possible upper bounds on a rich class of risk measures, expressible as integrals with respect to measures, under incomplete probabilistic information. Both univariate and multivariate risk measurement problems are considered. The extremal probability distributions, generating the worst case scenarios, are also identified.

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File URL: http://www.sciencedirect.com/science/article/pii/S0167668711000746
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Article provided by Elsevier in its journal Insurance: Mathematics and Economics.

Volume (Year): 49 (2011)
Issue (Month): 3 ()
Pages: 380-392

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Handle: RePEc:eee:insuma:v:49:y:2011:i:3:p:380-392
DOI: 10.1016/j.insmatheco.2011.06.001
Contact details of provider: Web page: http://www.elsevier.com/locate/inca/505554

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  3. Dhaene, J. & Denuit, M. & Goovaerts, M. J. & Kaas, R. & Vyncke, D., 2002. "The concept of comonotonicity in actuarial science and finance: theory," Insurance: Mathematics and Economics, Elsevier, vol. 31(1), pages 3-33, August.
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  13. Kaas, Rob & Laeven, Roger J.A. & Nelsen, Roger B., 2009. "Worst VaR scenarios with given marginals and measures of association," Insurance: Mathematics and Economics, Elsevier, vol. 44(2), pages 146-158, April.
  14. Goovaerts, M. J. & Haezendonck, J. & De Vylder, F., 1982. "Numerical best bounds on stop-loss preminus," Insurance: Mathematics and Economics, Elsevier, vol. 1(4), pages 287-302, October.
  15. Genest, Christian & Gerber, Hans U. & Goovaerts, Marc J. & Laeven, Roger J.A., 2009. "Editorial to the special issue on modeling and measurement of multivariate risk in insurance and finance," Insurance: Mathematics and Economics, Elsevier, vol. 44(2), pages 143-145, April.
  16. Laeven, Roger J.A., 2009. "Worst VaR scenarios: A remark," Insurance: Mathematics and Economics, Elsevier, vol. 44(2), pages 159-163, April.
  17. Goovaerts, Marc J. & Kaas, Rob & Dhaene, Jan & Tang, Qihe, 2003. "A Unified Approach to Generate Risk Measures," ASTIN Bulletin: The Journal of the International Actuarial Association, Cambridge University Press, vol. 33(02), pages 173-191, November.
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  20. Kaas, R. & Dhaene, J. & Vyncke, D. & Goovaerts, M.J. & Denuit, M., 2002. "A Simple Geometric Proof that Comonotonic Risks Have the Convex-Largest Sum," ASTIN Bulletin: The Journal of the International Actuarial Association, Cambridge University Press, vol. 32(01), pages 71-80, May.
  21. de Vylder, F. & Goovaerts, M., 1983. "Best bounds on the stop loss premium in case of known range, expectation, variance and mode of the risk," Insurance: Mathematics and Economics, Elsevier, vol. 2(4), pages 241-249, October.
  22. Goovaerts, Marc J. & Kaas, Rob & Laeven, Roger J.A., 2010. "Decision principles derived from risk measures," Insurance: Mathematics and Economics, Elsevier, vol. 47(3), pages 294-302, December.
  23. Paul Embrechts & Giovanni Puccetti, 2006. "Bounds for Functions of Dependent Risks," Finance and Stochastics, Springer, vol. 10(3), pages 341-352, September.
  24. Gerber, Hans U., 1974. "On Additive Premium Calculation Principles," ASTIN Bulletin: The Journal of the International Actuarial Association, Cambridge University Press, vol. 7(03), pages 215-222, March.
  25. De Vylder, F., 1983. "Maximization, under equality constraints, of a functional of a probability distribution," Insurance: Mathematics and Economics, Elsevier, vol. 2(1), pages 1-16, January.
  26. Embrechts, Paul & Hoing, Andrea & Puccetti, Giovanni, 2005. "Worst VaR scenarios," Insurance: Mathematics and Economics, Elsevier, vol. 37(1), pages 115-134, August.
  27. Goovaerts, Marc J. & Kaas, Rob & Laeven, Roger J.A., 2010. "A note on additive risk measures in rank-dependent utility," Insurance: Mathematics and Economics, Elsevier, vol. 47(2), pages 187-189, October.
  28. Denuit, Michel & Vylder, Etienne De & Lefevre, Claude, 1999. "Extremal generators and extremal distributions for the continuous s-convex stochastic orderings," Insurance: Mathematics and Economics, Elsevier, vol. 24(3), pages 201-217, May.
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