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高校应用数学学报
Applied Mathematics A Journal of Chinese Universities  2016, Vol. 31 Issue (3): 253-261    DOI:
    
Optimal reinsurance of a dependent mulit-type risk model under variance reinsurance premium principle
ZHANG Jie-song1,2, XIAO Qing-xian1
1. Business School, University of Shanghai for Science and Technology, Shanghai 200093, China
2. School of Management, Huaibei Normal University, Huaibei 235000, China
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Abstract  In this paper, the optimal reinsurance strategy is considered to minimize the ruin probability of a risk model with multiple dependent classes of insurance under variance reinsurance premium principle. Through diffusion approximation of the claim risk process and by applying the dynamic programming approach, explicit expressions of the optimal strategy and the value function are obtained. Moreover, by comparing to the results obtained under the expected value reinsurance premium principle, it is found that the optimal reinsurance form and the retention risk level are both different. By comparing to the results which maximize expected exponential utility, it is found that the optimal reinsurance proportion here depends not only on safety loading, but also on the claim distribution, the counting process and the premium rate of insurance $c$. Finally, combining with numerical example, dynamic impact of the dependence parameter is demonstrated and sensitive correlation between the optimal strategy and $c$ is illustrated.

Key words： variance reinsurance premium      dependent multi-type risk model      optimal reinsurance      ruin probability     
Received: 28 September 2015      Published: 16 May 2018
CLC:     
  O211.6  
  F84  
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ZHANG Jie-song
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ZHANG Jie-song, XIAO Qing-xian. Optimal reinsurance of a dependent mulit-type risk model under variance reinsurance premium principle. Applied Mathematics A Journal of Chinese Universities, 2016, 31(3): 253-261.

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http://www.zjujournals.com/amjcua/     OR     http://www.zjujournals.com/amjcua/Y2016/V31/I3/253


方差分保费原则下相依多险种模型的最优再保险

采用共同冲击型相依多险种模型刻画保险公司的索赔风险过程, 按照方差分保费原则计算再保险费, 研究最小化破产概率的再保险问题. 通过扩散逼近并利用动态规划原理, 得到了显式最优策略和值函数. 与采用期望值分保费原则比较, 发现最优分保形式和自留风险水平均不相同; 与最大化期望指数效用的结果比较, 发现最优分保比例除了与安全负载相关, 还与索赔分布、计数过程以及直接保险费收入率$c$有关. 最后, 结合数值算例揭示了相依参数的动态影响以及最优策略与$c$的敏感相关性.

关键词： 方差分保费原则,  相依多险种模型,  最优再保险,  破产概率 
[1] LI Hui-jie, NI Jia-lin, FU Ke-ang. Asymptotic estimates for the bidimensional time-dependent risk model with investments and by-claims[J]. Applied Mathematics A Journal of Chinese Universities, 2017, 32(3): 283-294.