两步法求解帕累托最优再保险策略
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摘要
基于风险价值准则,利用"两步法"研究保险人和再保险人的帕累托最优再保险策略.在分出损失函数和自留损失函数都满足单调递增的集合中,均给出了具体形式的帕累托最优再保险策略.
Based on the value at risk, the Pareto-optimal reinsurance strategy is studied for the insurer and the reinsurer by two step method. When the constraints on both ceded and retained loss functions are monotonically increasing, specific Pareto-optimal reinsurance strategies are given in all cases.
Based on the value at risk, the Pareto-optimal reinsurance strategy is studied for the insurer and the reinsurer by two step method. When the constraints on both ceded and retained loss functions are monotonically increasing, specific Pareto-optimal reinsurance strategies are given in all cases.
引文
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3 Cai J,Tan K S,Weng C G,et al.Optimal reinsurance under Va R and CTE risk measures[J].Insurance:Mathematics and Economics,2008,43(1):185-196.
4 Cheung K C.Optimal reinsurance revisited-a geometric approach[J].ASTIN Bulletin,2010,40(1):221-239.
5 Chi Y C,Tan K S.Optimal reinsurance under Va R and CVa R risk measures:a simplified approach[J].ASTIN Bulletin,2011,41(2):487-509.
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7 Borch K.An attempt to determine the optimum amount of stop loss reinsurance[J].Transactions of the 16th International Congress of Actuaries,1960,2:597-610.
8 Cai J,Fang Y,Li Z,et al.Optimal reciprocal reinsurance treaties under the joint survival probability and the joint profitable[J].Journal of Risk and Insurance,2013,80(1):145-168.
9 Fang Y,Qu Z F.Optimal combination of quota-share and stop-loss reinsurance treaties under the joint survival probability[J].IMA Journal of Management Mathematics,2014,25(1):89-103.
10 Cai J,Lemieux C,Liu F D.Optimal reinsurance from the perspectives of both an insurer and reinsurer[J].ASTIN Bulletin,2016,46(3):815-849.
11 Jiang W J,Ren J D,Zitikis R.Optimal reinsurance policies under the Va R risk measure when the interests of both the cedent and the reinsurer are taken into account[J].Risks,2017,5(1):1-10.
12 Asimit A V,Badescu A M,Verdonck T.Optimal risk transfer under quantile-based risk measurers[J].Insurance:Mathematics and Economics,2013,53(1):252-265.
2 Bowers N L,Gerber H U,James C H,et al.Actuarial mathematics[M].2nd ed.Schaumburg:Society of Actuaries,1997.
3 Cai J,Tan K S,Weng C G,et al.Optimal reinsurance under Va R and CTE risk measures[J].Insurance:Mathematics and Economics,2008,43(1):185-196.
4 Cheung K C.Optimal reinsurance revisited-a geometric approach[J].ASTIN Bulletin,2010,40(1):221-239.
5 Chi Y C,Tan K S.Optimal reinsurance under Va R and CVa R risk measures:a simplified approach[J].ASTIN Bulletin,2011,41(2):487-509.
6 Vajda S.Minimum variance reinsurance[J].ASTIN Bulletin,1962,2(2):257-260.
7 Borch K.An attempt to determine the optimum amount of stop loss reinsurance[J].Transactions of the 16th International Congress of Actuaries,1960,2:597-610.
8 Cai J,Fang Y,Li Z,et al.Optimal reciprocal reinsurance treaties under the joint survival probability and the joint profitable[J].Journal of Risk and Insurance,2013,80(1):145-168.
9 Fang Y,Qu Z F.Optimal combination of quota-share and stop-loss reinsurance treaties under the joint survival probability[J].IMA Journal of Management Mathematics,2014,25(1):89-103.
10 Cai J,Lemieux C,Liu F D.Optimal reinsurance from the perspectives of both an insurer and reinsurer[J].ASTIN Bulletin,2016,46(3):815-849.
11 Jiang W J,Ren J D,Zitikis R.Optimal reinsurance policies under the Va R risk measure when the interests of both the cedent and the reinsurer are taken into account[J].Risks,2017,5(1):1-10.
12 Asimit A V,Badescu A M,Verdonck T.Optimal risk transfer under quantile-based risk measurers[J].Insurance:Mathematics and Economics,2013,53(1):252-265.