有再保险控制下的非线性脉冲注资问题  

Nonlinear impulse capital injections problem with reinsurance control

作　　者：孟辉[1] 郭冬梅[2] 周明[1] 

机构地区：[1]中央财经大学中国精算研究院,北京100081 [2]中央财经大学经济学院,北京100081

出　　处：《中国科学：数学》2016年第2期235-246,共12页Scientia Sinica：Mathematica

基　　金：国家自然科学基金(批准号:11271385,71301173和11571388);教育部人文社会科学重点研究基地(批准号:14JJD790001);中央高校基本科研业务费专项资金;中央财经大学科研创新团队支持计划资助项目

摘　　要：假定有两家再保险公司共同接受原始保险公司的分保,且保险公司及这两家再保险公司均采用方差保费准则收取保费.基于上述跳风险模型,本文采用扩散逼近模型为基本模型来描述保险公司再保后的资产盈余.另外,为避免破产的发生,公司会接受外部资金注入.假定每次注资不低于某个固定常数d>0,且有固定交易费和比例费用,即为有限制情形下的脉冲注资.本文研究最小期望折现非线性脉冲注资问题,应用Hamilton-Jacobi-Bellman(HJB)方法,给出值函数和最优策略的明晰解答.最后,对有关参数进行灵敏度分析.Assume that two reinsurers participate in a reinsurance treaty, and both the insurer and two reinsur- ers adopt the variance premium principle. Based on the above jump risk model, we use the diffusion approximation risk process to model the assets of insurance company with reinsurance. To avoid bankruptcy, the insurance com- pany will receive capital injections, we assume that each capital injection is not less than a certain constant d 〉 0, and it also will incur some fixed transaction costs and proportional taxes, i.e., impulse injections with constraint. For the diffusion model, we study the minimum of the expected discounted nonlinear capital injection, using Hamiltou-Jacobi-Bellman （HJB） method, and we give explicit solutions for the value function and the optimal control strategy. Finally, for the influence of parameters on the optimal results, we also give numerical analysis.

关 键 词：方差保费准则 再保险策略 脉冲注资 非线性费用函数 HAMILTON-JACOBI-BELLMAN方程 

分 类 号：F842.3[经济管理—保险]