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Mathematical Problems in Engineering
Volume 2015, Article ID 143739, 12 pages
http://dx.doi.org/10.1155/2015/143739
Research Article

Optimal Limited Stop-Loss Reinsurance under VaR, TVaR, and CTE Risk Measures

1China Institute for Actuarial Science, Central University of Finance and Economics, Beijing 100081, China
2Research Institute of Applied Mathematics, Anhua Agricultural Insurance Co., Ltd., Beijing 100037, China
3School of Economics and Management, Tsinghua University, Beijing 100084, China

Received 27 April 2015; Revised 14 July 2015; Accepted 15 July 2015

Academic Editor: Xinguang Zhang

Copyright © 2015 Xianhua Zhou et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. K. Borch, “The safety loading of reinsurance premiums,” Scandinavian Actuarial Journal, no. 3-4, pp. 163–184, 1960. View at Google Scholar
  2. H. U. Gerber, An Introduction to Mathematical Risk Theory, vol. 8, SS Huebner Foundation for Insurance Education, Wharton School, University of Pennsylvania, Philadelphia, Pa, USA, 1979.
  3. L. Gajek and D. Zagrodny, “Insurer's optimal reinsurance strategies,” Insurance: Mathematics & Economics, vol. 27, no. 1, pp. 105–112, 2000. View at Publisher · View at Google Scholar · View at MathSciNet
  4. M. Kaluszka, “Mean-variance optimal reinsurance arrangements,” Scandinavian Actuarial Journal, no. 1, pp. 28–41, 2004. View at Publisher · View at Google Scholar · View at MathSciNet
  5. Y. Bu, “On optimal reinsurance arrangement,” in Casualty Actuarial Society Forum, pp. 1–20, 2005. View at Google Scholar
  6. J. Cai and K. S. Tan, “Optimal retention for a stop-loss reinsurance under the VaR and CTE risk measures,” Astin Bulletin, vol. 37, no. 1, pp. 93–112, 2007. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  7. J. Cai, K. S. Tan, C. Weng, and Y. Zhang, “Optimal reinsurance under VaR and CTE risk measures,” Insurance: Mathematics & Economics, vol. 43, no. 1, pp. 185–196, 2008. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  8. C. Weng, Optimal reinsurance designs: from an insurer's perspective [Ph.D. thesis], University of Waterloo, 2009.
  9. L. Fu and C. Khury, “Optimal layers for catastrophe reinsurance,” Variance, vol. 4, no. 2, pp. 191–208, 2010. View at Google Scholar
  10. Y. Chi and K. S. Tan, “Optimal reinsurance under VaR and CVaR Risk measures: a simplified approach,” Astin Bulletin, vol. 41, no. 2, pp. 487–509, 2011. View at Google Scholar · View at MathSciNet
  11. Y. Chi and C. Weng, “Optimal reinsurance subject to vajda condition,” Insurance: Mathematics and Economics, vol. 53, no. 1, pp. 179–189, 2013. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  12. L. Gajek and D. Zagrodny, “Optimal reinsurance under general risk measures,” Insurance: Mathematics and Economics, vol. 34, no. 2, pp. 227–240, 2004. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  13. M. Guerra and M. L. Centeno, “Optimal reinsurance policy: the adjustment coefficient and the expected utility criteria,” Insurance: Mathematics & Economics, vol. 42, no. 2, pp. 529–539, 2008. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  14. L. Porth, K. S. Tan, and C. Weng, “Optimal reinsurance analysis from a crop insurer's perspective,” Agricultural Finance Review, vol. 73, no. 2, pp. 310–328, 2013. View at Publisher · View at Google Scholar
  15. Q. Li, M. Gu, and Z. Liang, “Optimal excess-of-loss reinsurance and investment polices under the CEV model,” Annals of Operations Research, vol. 223, no. 1, pp. 273–290, 2014. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  16. M. Brandtner and W. Kürsten, “Solvency ii, regulatory capital, and optimal reinsurance: how good are conditional value-at-risk and spectral risk measures?” Insurance: Mathematics and Economics, vol. 59, pp. 156–167, 2014. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  17. C. Bernard and W. Tian, “Optimal reinsurance arrangements under tail risk measures,” Journal of Risk and Insurance, vol. 76, no. 3, pp. 709–725, 2009. View at Publisher · View at Google Scholar · View at Scopus
  18. P. Artzner, F. Delbaen, J.-M. Eber, and D. Heath, “Coherent measures of risk,” Mathematical Finance, vol. 9, no. 3, pp. 203–228, 1999. View at Publisher · View at Google Scholar · View at MathSciNet
  19. T. Hang, Actuarial Aspects of Non-Life Insurance, China Financial & Economic Publishing House, Beijing, China, 2010.
  20. A. Charpentier, Mesures de risque, Université Rennes 1, Rennes, France, 2010.
  21. J. L. Wirch and M. R. Hardy, “A synthesis of risk measures for capital adequacy,” Insurance: Mathematics and Economics, vol. 25, no. 3, pp. 337–347, 1999. View at Publisher · View at Google Scholar · View at Scopus