风险相依下再保险双方的联合最优再保险问题

doi:10.15960/j.cnki.issn.1007-6093.2019.04.002

运筹学学报 ›› 2019, Vol. 23 ›› Issue (4): 13-33.doi: 10.15960/j.cnki.issn.1007-6093.2019.04.002

风险相依下再保险双方的联合最优再保险问题

黄娅^1,2, 王京², 周杰明², 邓迎春^2,*

1. 湖南师范大学商学院, 长沙 410081;
2. 计算与随机数学教育部重点实验室, 湖南师范大学数学与统计学院, 长沙 410081

收稿日期:2017-11-29 发布日期:2019-12-04
通讯作者: 邓迎春 E-mail:dengyc@hunnu.edu.cn
基金资助:
湖南省哲学社会科学基金（No.17YBA290），湖南省教育厅科学研究项目（Nos.17K057，17C1001）

The optimal reinsurance problem towards joint interests of the insurer and the reinsurer with dependent risks

HUAGN Ya^1,2, WANG Jing², ZHOU Jieming², DENG Yingchun^2,*

1. School of Business, Hunan Normal University, Changsha 410081, China;
2. Key Laboratory of Computing and Stochastic Mathematics(Ministry of Education), School of Mathematics and Statistics, Hunan Normal University, Changsha 410081, China

Received:2017-11-29 Published:2019-12-04

摘要/Abstract

摘要： 结合保险人和再保险人的共同利益，研究了具有两类相依险种风险模型下的最优再保险问题.假定再保险公司采用方差保费原理收取保费，利用复合Poisson模型和扩散逼近模型两种方式去刻画保险公司和再保险公司的资本盈余过程，在期望效用最大准则下，证明了最优再保险策略的存在性和唯一性，通过求解Hamilton-Jacobi-Bellman（HJB）方程，得到了两种模型下相应的最优再保险策略及值函数的明晰解答，并给出了数值算例及分析.

关键词: 盈余过程, 再保险, 方差保费原理, 相依索赔, 期望效用

Abstract: In this paper, by considering the joint interests of the insurer and the reinsurer, we study the optimal reinsurance problem in a risk model with two dependent classes of insurance business. Assume that the reinsurance company adopts the variance premium principle. The surplus processes of the insurance company and the reinsurance company are both governed by the compound Poisson model as well as by the diffusion approximation model. Under the criterion of maximizing the expected utility, we prove the existence and uniqueness of the optimal reinsurance strategies. By solving the corresponding Hamilton-Jacobi-Bellman equations, closed-form expressions for the optimal reinsurance strategies and the value functions are derived for the two models. Moreover, we also present numerical examples and analysis.

Key words: surplus process, reinsurance, variance premium principle, dependent claims, expected utility

中图分类号:

O211.67

黄娅, 王京, 周杰明, 邓迎春. 风险相依下再保险双方的联合最优再保险问题[J]. 运筹学学报, 2019, 23(4): 13-33.

HUAGN Ya, WANG Jing, ZHOU Jieming, DENG Yingchun. The optimal reinsurance problem towards joint interests of the insurer and the reinsurer with dependent risks[J]. Operations Research Transactions, 2019, 23(4): 13-33.

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风险相依下再保险双方的联合最优再保险问题

The optimal reinsurance problem towards joint interests of the insurer and the reinsurer with dependent risks

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