226
Views
3
CrossRef citations to date
0
Altmetric
Original Articles

Optimal reinsurance from the perspectives of both insurers and reinsurers under the VaR risk measure and Vajda condition

&
Pages 3677-3694 | Received 08 Mar 2019, Accepted 24 Dec 2019, Published online: 20 Jan 2020

References

  • Arrow, K. 1963. Uncertainty and the welfare economics of medical care. American Economic Review 53 (5):941–73.
  • Barlow, R. E., and F. Proschan. 1981. Statistical theory of reliability and life testing: probability models. To begin with. Boston, MD: Sliver Springs.
  • Borch, K. 1960. Reciprocal reinsurance treaties seen as a two-person co-operative game. Scandinavian Actuarial Journal 1960 (1–2):29–58. doi:10.1080/03461238.1960.10410597.
  • Borch, K. 1969. The optimal reinsurance treaty. Astin Bulletin 5 (2):293–7. doi:10.1017/S051503610000814X.
  • Cai, J., Y. Fang, Z. Li, and G. Willmot. 2013. Optimal reciprocal reinsurance treaties under the joint survival probability and the joint probability. Journal of Risk and Insurance 80 (1):145–68. doi:10.1111/j.1539-6975.2012.01462.x.
  • Cai, J., C. Lemieux, and F. Liu. 2016. Optimal reinsurance from the perspectives of both an insurer and a reinsurer. Astin Bulletin 46 (3):815–49. doi:10.1017/asb.2015.23.
  • Cai, J., H. Liu, and R. Wang. 2017. Pareto-optimal reinsrance arrangements under general model settings. Insurance: Mathematics and Economics 77:24–37. doi:10.1016/j.insmatheco.2017.08.004.
  • Cai, J., and K. Tan. 2007. Optimal retention for a stop-loss reinsurance under the VaR and CTE risk measures. Astin Bulletin 37 (1):93–112. doi:10.1017/S0515036100014756.
  • Chi, Y., and K. Tan. 2013. Optimal reinsurance with general premium principles. Insurance: Mathematics and Economics 52 (2):180–9. doi:10.1016/j.insmatheco.2012.12.001.
  • Chi, Y., and C. Weng. 2013. Optimal reinsurance subject to Vajda condition. Insurance: Mathematics and Economics 53:179–89. doi:10.1016/j.insmatheco.2013.05.002.
  • Dhaene, J., M. Denuit, M. J. Goovaerts, R. Kaas, and D. Vyncke. 2002. The concept of comonotonicity in acturial science and finance: Theory. Insurance: Mathematics and Economics 31 (1):3–33. doi:10.1016/S0167-6687(02)00134-8.
  • Fang, Y., and Z. Qu. 2014. Optimal combination of quota-share and stop-loss reinsurance treaties under the joint survival probability. IMA Journal of Management Mathematics 25 (1):89–103. doi:10.1093/imaman/dps029.
  • Föllmer, H., and A. Schied. 2004. Stochastic finance, an introduction in discrete time. 2nd revised and extended edition. Berlin, NY: Welter de Gruyter.
  • Hesselager, O. 1990. Some results on optimal reinsurance in terms of the adjustment coefficient. Scandinavian Actuarial Journal 1:80–95. doi:10.1080/03461238.1990.10413873.
  • Hesselager, O. 1993. Extensions of Ohlin’s lemma with applications to optimal reinsurance structures. Insurance: Mathematics and Economics 13 (1):83–97. doi:10.1016/0167-6687(93)90538-Z.
  • Huang, Y., and C. Yin. 2019. A unifying approach to constrained and unconstrained optimal reinsurance. Journal of Computational and Applied Mathematics 360:1–17. doi:10.1016/j.cam.2019.03.046.
  • Huberman, G., D. Mayers, and C. Smith. 1983. Optimal insurance policy indemnity schedules. The Bell Journal of Economics 14 (2):415–26. doi:10.2307/3003643.
  • Hürlimann, W. 2011. Optimal reinsurance revisited -point of view of ceded and reinsurer. Astin Bulletin 41 (2):547–74.
  • Jiang, W., H. Hong, and J. Ren. 2018. On pareto-optimal reinsurance with constraints under distortion risk measures. European Actuarial Journal 8 (1):215–43. doi:10.1007/s13385-017-0163-1.
  • Jiang, W., J. Ren, and R. Zitikis. 2017. Optimal reinsurance policies under the VaR risk measure when the interests of both the cedent and the reinsurer are taken into account. Risks 5 (1):11. doi:10.3390/risks5010011.
  • Lo, A., and Z. Tang. 2019. Pareto-optimal reinsurance policies in the presence of individual risk constraints. Annals of Operations Research 274 (1–2):395–423. doi:10.1007/s10479-018-2820-4.
  • Ohlin, J. 1969. On a class of measures of dispersion with application to optimal reinsurance. Astin Bulletin 5 (2):249–66. doi:10.1017/S0515036100008102.
  • Vajda, S. 1962. Minimum variance reinsurance. Astin Bulletin 2 (2):257–60. doi:10.1017/S0515036100009995.
  • Young, V. 2004. Premium principles. In Encyclopedia of actuarial science, ed. J. Teugels, B. Sundt. Vol. 3. Hoboken, NJ: John Wiley & Sons.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.