| 基于Esscher保费原理的风险最优分配决策 |
| Optimal allocation of risks based on Esscher premium principle |
| 摘要点击 22 全文点击 0 投稿时间：2022-07-16 修订日期：2024-03-01 |
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| 中文关键词 风险分配；Esscher保费原理；优化； 二次距离 |
| 英文关键词 Risk allocation; Esscher premium principle; Optimization; Quadratic distance |
| 基金项目 融入机器学习算法的保费厘定及其应用研究；相依模型中风险保费的经验厘定及其应用研究 |
| 作者 | 单位 | 邮编 | | 温利民 | 江西师范大学数学与统计学院 | 330022 | | 崔梦琪 | 楚雄师范学院 | |
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| 中文摘要 |
| 在加权二次分配原则中引入了Esscher保费原理, 建立了该保费原理下的保单组合的风险分配模型, 并讨论了保费分配的次可加性条件, 得到了基于Esscher 保费原理的总保费的最优分配方案. 经过分析和对比, 本文给出的最优分配方案不仅能给出加权二次分配原则的理论解释, 而且给出的最优分配结果比已有的分配方案更能体现风险与保费的贴近程度. 进而, 研究了风险的分布未知时最优分配方案的估计, 并证明了估计的大样本性质. 最后, 根据实际数据获得的均值和方差矩阵, 将各种分配方案进行了对比, 并验证了估计的相合性和渐近正态性. |
| 英文摘要 |
| The Esscher premium principle is introduced into the weighted quadratic allocation principle, the risk allocation model of the policy portfolio under the premium principle is established, and the sub-additivity condition of the premium allocation is discussed.
The optimal allocation scheme of total premium based on Esscher's premium principle is obtained.
After analysis and comparison, the optimal allocation scheme given in this paper can not only give a theoretical explanation of the weighted quadratic allocation principle, but also the optimal allocation result can reflect the closeness of risk and premium more than the existing allocation scheme. Furthermore, the estimation of the optimal allocation scheme when the distribution of risk is unknown is studied, and the large sample properties of the estimation are proved. Finally, based on the mean and variance matrices obtained from the actual data, various allocation schemes are compared and the estimated consistency and asymptotic normality are verified. |
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