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Articles

Equilibrium excess-of-loss reinsurance and investment strategies for an insurer and a reinsurer

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Pages 7496-7527 | Received 23 May 2020, Accepted 31 Dec 2020, Published online: 18 Feb 2021

References

  • Asmussen, S., B. Højgaard, and M. Taksar. 2000. Optimal risk control and dividend distribution policies: Example of excess-of-loss reinsurance for an insurance corporation. Finance and Stochastics 4 (3):299–324. doi:10.1007/s007800050075.
  • Bäerle, N. 2005. Benchmark and mean-variance problems for insurers. Mathematical Methods of Operations Research 62 (1):159–65.
  • Bai, L., J. Cai, and M. Zhou. 2013. Optimal reinsurance policies for an insurer with a bivariate reserve risk process in a dynamic setting. Insurance: Mathematics and Economics 53 (3):664–70. doi:10.1016/j.insmatheco.2013.09.008.
  • Bai, L., and J. Guo. 2010. Optimal dynamic excess-of-loss reinsurance and multidimensional portfolio selection. Science China Mathematics 53 (7):1787–804. doi:10.1007/s11425-010-4033-4.
  • Bai, L., and H. Zhang. 2008. Dynamic mean-variance problem with constrained risk control for the insurers. Mathematical Methods of Operations Research 68 (1):181–205. doi:10.1007/s00186-007-0195-4.
  • Bayraktar, E., and Y. Zhang. 2015. Minimizing the probability of life time ruin under ambiguity aversion. SIAM Journal on Control and Optimization 53 (1):58–90. doi:10.1137/140955999.
  • Björk, T., and A. Murgoci. 2010. A general theory of Markovian time inconsistent stochastic control problems. Working Paper. https://papers.ssrn.com/sol3/papers.cfm?abstract_id=1694759.
  • Cai, J., Y. Fang, Z. Li, and G. E. Willmot. 2013. Optimal reciprocal reinsurance treaties under the joint survival probability and the joint profitable probability. Journal of Risk and Insurance 80 (1):145–68. doi:10.1111/j.1539-6975.2012.01462.x.
  • Chen, L., and Y. Shen. 2018. On a new paradigm of optimal reinsurance: A stochastic Stackelberg differential game between an insurer and a reinsurer. ASTIN Bulletin 48 (02):905–60. doi:10.1017/asb.2018.3.
  • Chen, L., and Y. Shen. 2019. Stochastic Stackelberg differential reinsurance games under time-inconsistent mean-variance framework. Insurance: Mathematics and Economics 88:120–37. doi:10.1016/j.insmatheco.2019.06.006.
  • Chen, L., Y. Shen, and J. Su. 2020. A continuous-time theory of reinsurance chains. Insurance: Mathematics and Economics 95:129–146. doi:10.1016/j.insmatheco.2019.06.006.
  • Chen, S., Z. Li, and K. Li. 2010. Optimal investment-reinsurance policy for an insurance company with VaR constraint. Insurance: Mathematics and Economics 47 (2):144–53. doi:10.1016/j.insmatheco.2010.06.002.
  • Dimitrova, D. S., and V. K. Kaishev. 2010. Optimal joint survival reinsurance: An efficient frontier approach. Insurance: Mathematics and Economics 47 (1):27–35. doi:10.1016/j.insmatheco.2010.03.006.
  • Eraker, B., M. Johannes, and N. Polson. 2003. The impact of jumps in volatility and returns. The Journal of Finance 58 (3):1269–300. doi:10.1111/1540-6261.00566.
  • 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.
  • French, K. R., G. W. Schwert, and R. F. Stambaugh. 1987. Expected stock returns and volatility. Journal of Financial Economics 19 (1):3–29. doi:10.1016/0304-405X(87)90026-2.
  • Gerber, H. U. 1979. An introduction to mathematical risk theory. S.S. Philadelphia, PA: Huebner Foundation Monographs, University of Pennsylvania.
  • Golubin, A. Y. 2006. Pareto-optimal insurance policies in the models with a premium based on the actuarial value. Journal of Risk and Insurance 73 (3):469–87. doi:10.1111/j.1539-6975.2006.00184.x.
  • Gu, A., X. Guo, Z. Li, and Y. Zeng. 2012. Optimal control of excess-of-loss reinsurance and investment for insurers under a CEV model. Insurance: Mathematics and Economics 51 (3):674–84. doi:10.1016/j.insmatheco.2012.09.003.
  • Gu, A., F. G. Viens, and Y. Shen. 2020. Optimal excess-of-loss reinsurance contract with ambiguity aversion in the principal-agent model. Scandinavian Actuarial Journal 2020 (4):342–75. doi:10.1080/03461238.2019.1669218.
  • Hu, D., S. Chen, and H. Wang. 2018. Robust reinsurance contracts in continuous time. Scandinavian Actuarial Journal 2018 (1):1–22. doi:10.1080/03461238.2016.1274270.
  • Hu, D., and H. Wang. 2019. Reinsurance contract design when the insurer is ambiguity-averse. Insurance: Mathematics and Economics 86:241–55. doi:10.1016/j.insmatheco.2019.03.007.
  • Kryger, E., and M. Steffensen. 2010. Some solvable portfolio problems with quadratic and collective objectives. Working Paper. https://ssrn.com/abstract=1577265.
  • Li, D., X. Rong, and H. Zhao. 2015. Time-consistent reinsurance-investment strategy for an insurer and a reinsurer with mean-variance criterion under the CEV model. Journal of Computational and Applied Mathematics 283:142–62. doi:10.1016/j.cam.2015.01.038.
  • Li, D., X. Rong, and H. Zhao. 2017. Equilibrium excess-of-loss reinsurance-investment strategy for a mean-variance insurer under stochastic volatility model. Communications in Statistics - Theory and Methods 46 (19):9459–75. doi:10.1080/03610926.2016.1212071.
  • Li, Z., Y. Zeng, and Y. Lai. 2012. Optimal time-consistent investment and reinsurance strategies for insurers under Heston’s SV model. Insurance: Mathematics and Economics 51 (1):191–203. doi:10.1016/j.insmatheco.2011.09.002.
  • Liang, Z., and E. Bayraktar. 2014. Optimal reinsurance and investment with unobservable claim size and intensity. Insurance: Mathematics and Economics 55:156–66. doi:10.1016/j.insmatheco.2014.01.011.
  • Liang, Z., and K. C. Yuen. 2016. Optimal dynamic reinsurance with dependent risks: Variance premium principle. Scandinavian Actuarial Journal 2016 (1):18–36. doi:10.1080/03461238.2014.892899.
  • Liu, Y., and J. Ma. 2009. Optimal reinsurance/investment problems for general insurance models. The Annals of Applied Probability 19 (4):1495–528. doi:10.1214/08-AAP582.
  • Promislow, S. D., and V. R. Young. 2005. Minimizing the probability of ruin when claims follow Brownian motion with drift. North American Actuarial Journal 9 (3):110–28. doi:10.1080/10920277.2005.10596214.
  • Shen, Y., and Y. Zeng. 2015. Optimal investment-reinsurance strategy for mean-variance insurers with square-root factor process. Insurance: Mathematics and Economics 62:118–37. doi:10.1016/j.insmatheco.2015.03.009.
  • Siu, C. C., S. C. P. Yam, H. Yang, and H. Zhao. 2017. A class of nonzero-sum investment and reinsurance games subject to systematic risks. Scandinavian Actuarial Journal 2017 (8):670–707. doi:10.1080/03461238.2016.1228542.
  • Wang, N., and T. K. Siu. 2020. Robust reinsurance contracts in continuous time. Scandinavian Actuarial Journal 2020 (5):419–53. doi:10.1080/03461238.2019.1683761.
  • Young, V. R. 2004. Optimal investment strategy to minimize the probability of life time ruin. North American Actuarial Journal 8 (4):106–26. doi:10.1080/10920277.2004.10596174.
  • Zhang, N., Z. Jin, L. Qian, and R. Wang. 2018. Optimal quota-share reinsurance based on the mutual benefit of insurer and reinsurer. Journal of Computational and Applied Mathematics 342:337–51. doi:10.1016/j.cam.2018.04.030.
  • Zeng, X., and S. Luo. 2013. Stochastic Pareto-optimal reinsurance policies. Insurance: Mathematics and Economics 53 (3):671–77. doi:10.1016/j.insmatheco.2013.09.006.
  • Zeng, Y., and Z. Li. 2011. Optimal time-consistent investment and reinsurance policies for mean-variance insurers. Insurance: Mathematics and Economics 49 (1):145–54. doi:10.1016/j.insmatheco.2011.01.001.
  • Zhao, H., X. Rong, and Y. Zhao. 2013. Optimal excess-of-loss reinsurance and investment problem for an insurer with jump-diffusion risk process under the Heston model. Insurance: Mathematics and Economics 53 (3):504–14. doi:10.1016/j.insmatheco.2013.08.004.
  • Zhou, J., X. Yang, and Y. Huang. 2017. Robust optimal investment and proportional reinsurance towards joint interests of the insurer and the reinsurer. Communications in Statistics - Theory and Methods 46 (21):10733–57. doi:10.1080/03610926.2016.1242734.

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