Multivariate Insurance Portfolio Risk Retention Using the Method of Multipliers

REFERENCES

• Arrow, K. J. 1974. Optimal insurance and generalized deductibles. Scandinavian Actuarial Journal 1:1–42. doi:10.1080/03461238.1974.10408659
   Google Scholar
• Asimit, A. V., A. M. Badescu, and T. Verdonck. 2013. Optimal risk transfer under quantile-based risk measures. Insurance: Mathematics and Economics 53:252–65. doi:10.1016/j.insmatheco.2013.05.005
   Web of Science ®Google Scholar
• Assa, H. 2015. On optimal reinsurance policy with distortion risk measures and premiums. Insurance: Mathematics and Economics 61:70–75. doi:10.1016/j.insmatheco.2014.11.007
   Web of Science ®Google Scholar
• Bauer, D., and G. Zanjani. 2013. Capital allocation and its discontents. In Handbook of insurance, ed. G. Dionne, 863–80. New York: Springer.
   Google Scholar
• Bauer, D., and G. Zanjani. 2016. The marginal cost of risk, risk measures, and capital allocation. Management Science 62 (5):1431–57. doi:10.1287/mnsc.2015.2190
   Web of Science ®Google Scholar
• Borch, K. 1960. An attempt to determine the optimum amount of stop loss reinsurance. Transactions of the 16th International Congress of Actuaries 1 (3):597–610.
   Google Scholar
• Bowers, N., H. Gerber, J. Hickman, D. Jones, and C. Nesbitt. 1997. Actuarial mathematics. Vol. 2. Schaumburg, IL: The Society of Actuaries.
   Google Scholar
• Boyd, S., N. Parikh, E. Chu, B. Peleato, and J. Eckstein. 2010. Distributed optimization and statistical learning via the alternating direction method of multipliers. Foundations and Trends in Machine Learning 3 (1):1–122. doi:10.1561/2200000016
   Google Scholar
• Boyd, S., and L. Vandenberghe. 2004. Convex optimization. Cambridge, UK: Cambridge University Press.
   Google Scholar
• Cai, J., C. Lemieux, and F. Liu. 2015. Optimal reinsurance from the perspectives of both an insurer and a reinsurer. ASTIN Bulletin 46 (3):815–49. doi:10.1017/asb.2015.23
   Web of Science ®Google Scholar
• Cai, J., H. Liu, and R. Wang. 2017. Pareto-optimal reinsurance arrangements under general model settings. Insurance: Mathematics and Economics 77 (2017):24–37. doi:10.1016/j.insmatheco.2017.08.004
   Google Scholar
• Cai, J., and K. S. 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
   Web of Science ®Google Scholar
• Cai, J., K. S. Tan, C. Weng, and Y. Zhang. 2008. Optimal reinsurance under VaR and CTE risk measures. Insurance: Mathematics and Economics 43:185–96. doi:10.1016/j.insmatheco.2008.05.011
   Web of Science ®Google Scholar
• Cai, J., and W. Wei. 2012. Optimal reinsurance with positively dependent risks. Insurance: Mathematics and Economics 50:57–63. doi:10.1016/j.insmatheco.2011.10.006
   Web of Science ®Google Scholar
• Daykin, C., T. Pentiakainen, and M. Pesonen. 1994. Practical risk theory for actuaries. London: Chapman and Hall.
   Google Scholar
• Dhaene, J., A. Tsanakas, E. Valdez, and S. Vanduffel. 2012. Optimal capital allocation principles. Journal of Risk and Insurance 79 (1):1–28. doi:10.1111/j.1539-6975.2011.01408.x
   Web of Science ®Google Scholar
• Embrechts, P., H. Liu, and R. Wang. 2018. Quantile-based risk sharing. Operations Research 66 (4):936–49. doi:10.1287/opre.2017.1716
   Web of Science ®Google Scholar
• Frees, E. W. 2017. Insurance portfolio risk retention. North American Actuarial Journal 21 (2):526–51. doi:10.1080/10920277.2017.1317272
   Google Scholar
• Frees, E. W., G. Lee, and L. Yang. 2016. Multivariate frequency-severity regression models in insurance. Risks 4 (1). doi:10.3390/risks4010004
   Google Scholar
• Gollier, C. 2013. The economics of optimal insurance design. In Handbook of insurance, ed. G. Dionne, 107–22. 2nd ed. New York: Springer.
   Google Scholar
• Gray, R. J., and S. M. Pitts. 2012. Risk modelling in general insurance: From principles to practice. Cambridge, UK: Cambridge University Press.
   Google Scholar
• Hong, J. L. 2009. Estimating quantile sensitivities. Operations Research 57 (1):118–30. doi:10.1287/opre.1080.0531
   Web of Science ®Google Scholar
• Jeong, H. 2020. Testing for random effects in compound risk models via Bregman divergence. ASTIN Bulletin 50 (3):777–98. doi:10.1017/asb.2020.19
   Web of Science ®Google Scholar
• Kaas, R., M. Goovaerts, J. Dhaene, and M. Denuit. 2009. Modern actuarial risk theory using R. 2nd ed. Heidelberg, Germany: Springer.
   Google Scholar
• Mossin, J. 1968. Aspects of rational insurance purchasing. Journal of Political Economy 76 (4):553–68. doi:10.1086/259427
   Web of Science ®Google Scholar
• Schlesinger, H. 2013. The theory of insurance demand. In Handbook of insurance, ed. G. Dionne, 167–84. New York: Springer.
   Google Scholar
• Shi, P., and G. Lee. 2022. Copula regression for compound distributions with endogenous covariates with applications in insurance deductible pricing. Journal of the American Statistical Association 117 (539):1094–109. doi:10.1080/01621459.2022.2040519
   PubMed Web of Science ®Google Scholar
• Sung, K., S. Yam, S. Yung, and J. Zhou. 2011. Behavioral optimal insurance. Insurance: Mathematics and Economics 49:418–28. doi:10.1016/j.insmatheco.2011.04.008
   Web of Science ®Google Scholar