Optimal reinsurance design under solvency constraints

References

• Albrecher, H., Beirlant, J. & Teugels, J. L. (2017). Reinsurance: actuarial and statistical aspects. Hoboken, NJ: John Wiley & Sons.
   Google Scholar
• Albrecher, H. & Thonhauser, S. (2009). Optimality results for dividend problems in insurance. RACSAM Revista de la Real Academia de Ciencias; Serie A, Mathemáticas 100(2), 295–320.
   Google Scholar
• Arrow, K. J. (1963). Uncertainty and the welfare economics of medical care. The American Economic Review 53(5), 941–973.
   Web of Science ®Google Scholar
• Asimit, V. & Boonen, T. J. (2018). Insurance with multiple insurers: a game-theoretic approach. European Journal of Operational Research 267(2), 778–790.
   Web of Science ®Google Scholar
• Asmussen, S. & Albrecher, H. (2010). Ruin probabilities, 2nd ed. Vol. 14 of advanced series on statistical science and applied probability. Singapore: World Scientific Singapore.
   Google Scholar
• Avanzi, B. (2009). Strategies for dividend distribution: a review. North American Actuarial Journal 13(2), 217–251.
   Google Scholar
• Bai, Y., Zhou, Z., Xiao, H., Gao, R. & Zhong, F. (2022). A hybrid stochastic differential reinsurance and investment game with bounded memory. European Journal of Operational Research 296(2), 717–737.
   Web of Science ®Google Scholar
• Balbás, A., Balbás, B. & Balbás, R. (2021). Omega ratio optimization with actuarial and financial applications. European Journal of Operational Research 292(1), 376–387.
   Web of Science ®Google Scholar
• Balbás, A., Balbás, B. & Heras, A. (2009). Optimal reinsurance with general risk measures. Insurance: Mathematics and Economics 44(3), 374–384.
   Web of Science ®Google Scholar
• Balbás, A., Balbás, B. & Heras, A. (2011). Stable solutions for optimal reinsurance problems involving risk measures. European Journal of Operational Research 214(3), 796–804.
   Web of Science ®Google Scholar
• Basak, S. & Shapiro, A. (2001). Value-at-risk-based risk management: optimal policies and asset prices. Review of Financial Studies 14(2), 371–405.
   Web of Science ®Google Scholar
• Bäuerle, N. (2004a). Approximation of optimal reinsurance and dividend payout policies. Mathematical Finance 14(1), 99–113.
   Web of Science ®Google Scholar
• Bäuerle, N. (2004b). Traditional versus non-traditional reinsurance in a dynamic setting. Scandinavian Actuarial Journal 2004(5), 355–371.
   Google Scholar
• Bühlmann, H. (1970). Mathematical methods in risk theory. Grundlehren der mathematischen Wissenschaften. Berlin, Heidelberg, New York: Springer-Verlag.
   Google Scholar
• Cai, J. & Chi, Y. (2020). Optimal reinsurance designs based on risk measures: a review. Statistical Theory and Related Fields 4(1), 1–13.
   Google Scholar
• Cao, J., Landriault, D. & Li, B. (2020). Optimal reinsurance-investment strategy for a dynamic contagion claim model. Insurance: Mathematics and Economics 93, 206–215.
   Web of Science ®Google Scholar
• Cramér, H. (1955). Collective risk theory: a survey of the theory from the point of view of the theory of stochastic processes. Stockholm: Ab Nordiska Bokhandeln.
   Google Scholar
• de Finetti, B. (1957). Su un'impostazione alternativa della teoria collettiva del rischio. Transactions of the XVth International Congress of Actuaries 2, 433–443.
   Google Scholar
• Eckert, J. & Gatzert, N. (2018). Risk- and value-based management for non-life insurers under solvency constraints. European Journal of Operational Research 266(2), 761–774.
   Web of Science ®Google Scholar
• Fahrenwaldt, M. & Sun, C. (2020). Expected utility approximation and portfolio optimisation. Insurance: Mathematics and Economics 93, 301–314.
   Web of Science ®Google Scholar
• Gerber, H. U. (1972). Games of economic survival with discrete- and continuous-income processes. Operations Research 20(1), 37–45.
   Web of Science ®Google Scholar
• Gu, J.-W., Steffensen, M. & Zheng, H. (2021). A note on P- vs. Q-expected loss portfolio constraints. Quantitative Finance 21(2), 263–270.
   Web of Science ®Google Scholar
• Guan, C., Xu, Z. Q. & Zhou, R. (2022). Dynamic optimal reinsurance and dividend payout in finite time horizon. Mathematics of Operations Research 48(1), 544–568.
   Web of Science ®Google Scholar
• Karatzas, I., Lehoczky, J., Sethi, S. & Shreve, S. (1986). Explicit solution of a general consumption/investment problem. In N., C., K., H., M., K. (Eds.), Stochastic Differential Systems. Lecture Notes in Control and Information Sciences. Vol. 78. Berlin, Heidelberg: Springer.
   Google Scholar
• Korn, R. (1997). Optimal porfolios: stochastic models for optimal investment and risk management in continuous time. Singapore: World Scientific Publishing Company.
   Google Scholar
• Korn, R. (2005). Optimal portfolios with a positive lower bound on final wealth. Quantitative Finance 5(3), 315–321.
   Web of Science ®Google Scholar
• Korn, R. & Wiese, A. (2008). Optimal investment and bounded ruin probability: constant portfolio strategies and mean-variance analysis. ASTIN Bulletin 38(2), 423–440.
   Web of Science ®Google Scholar
• Kraft, H. & Steffensen, M. (2013). A dynamic programming approach to constrained portfolios. European Journal of Operational Research 229(2), 453–461.
   Web of Science ®Google Scholar
• Li, D., Li, D. & Young, V. R. (2017). Optimality of excess-loss reinsurance under a mean-variance criterion. Insurance: Mathematics and Economics 75, 82–89.
   Web of Science ®Google Scholar
• Lundberg, F. (1909). Über die Theorie der Rückversicherung. Transactions of the VIth International Congress of Actuaries 1, 877–948.
   Google Scholar
• Merton, R. C. (1969). Lifetime portfolio selection under uncertainty: the continuous-time case. The Review of Economics and Statistics 51(3), 247–257.
   Web of Science ®Google Scholar
• Nordfang, M.-B. & Steffensen, M. (2017). Approximations to expected utility optimization in continuous time. Available at SSRN:doi 10.2139/ssrn.2945313
   Google Scholar
• Øksendal, B. & Sulem, A. (2010). Applied stochastic control of jump diffusions, 2nd ed. Berlin: Springer.
   Google Scholar
• Redington, F. M. (1952). Review of the principles of life-office valuations. Journal of the Institute of Actuaries 78(3), 286–340.
   Google Scholar
• Reichel, L., Schmeiser, H. & Schreiber, F. (2021). Sometimes more, sometimes less: prudence and the diversification of risky insurance coverage. European Journal of Operational Research 292(2), 770–783.
   Web of Science ®Google Scholar
• Schmidli, H. (2008). Stochastic control in insurance. Probability and its applications. Berlin, Heidelberg, New York: Springer.
   Google Scholar
• Steffensen, M. (2006). Quadratic optimization of life and pension insurance payments. ASTIN Bulletin 36(1), 245–267.
   Web of Science ®Google Scholar
• Tan, K. S., Wei, P., Wei, W. & Zhuang, S. C. (2020). Optimal dynamic reinsurance policies under a generalized Denneberg's absolute deviation principle. European Journal of Operational Research 282(1), 345–362.
   Web of Science ®Google Scholar
• Zhang, X., Meng, H. & Zeng, Y. (2016). Optimal investment and reinsurance strategies for insurers with generalized mean-variance premium principle and no-short selling. Insurance: Mathematics and Economics 67, 125–132.
   Web of Science ®Google Scholar