Poisson-Geometric模型下时间一致的最优再保险-投资策略选择  

Time-Consistent Optimal Reinsurance-Investment Strategy Selection for Poisson-Geometric Model

作　　者：杨鹏[1,2] 杨志江 孔祥鑫 YANG Peng;YANG Zhijiang;KONG Xiangxin(School of Science, Xijing University, Xi'an 710123, China;School of Mathematicsand Statistics, Xi'an Jiaotong University, Xi'an 710049, China;Department of Electrical, Weifang Engineering Technician College, Zhucheng 262233, China;School of Mizhou Road in Zhucheng, Zhucheng 262233, China)

机构地区：[1]西京学院理学院,陕西西安710123 [2]西安交通大学数学与统计学院,陕西西安710049 [3]潍坊市工程技师学院电气系,山东诸城262233 [4]诸城市密州路学校,山东诸城262233

出　　处：《应用数学》2019年第4期729-738,共10页Mathematica Applicata

基　　金：国家自然科学基金资助(11726624)

摘　　要：本文研究Poisson-Geometric模型下,时间一致的再保险-投资策略选择问题.在风险模型中,理赔发生次数用Poisson-Geometric过程描述,保险公司在进行再保险时,按照方差值原理计算再保险的保费.保险人在金融市场上投资时,风险资产满足带跳的随机微分方程.保险人的目标是,选择一个时间一致的再保险-投资策略,最大化终止时刻财富的均值同时最小化其方差.通过使用随机控制理论,求得时间一致的再保险-投资策略以及值函数的显式解.最后分析结果的经济意义,并通过数值计算,解释了模型参数对最优策略的影响.In this paper, a time-consistent reinsurance-investment strategy selection for Poisson- Geometric model is considered. In risk model, the number of claims is a Poisson-Geometric process. When reinsurance is carried out by the insurance company , the premium of reinsurance should be calculated according to the variance principle. When the insurer invest in nancial market, the risky asset is assumed to follow a stochastic di erential equation with jump. The ob jective of the insurer is to choose an optimal time-consistent reinsurance-investment strategy so as to maximize the expected terminal wealth while minimizing the variance of the terminal wealth. W e investigate the problem using the stochastic control theory . Explicit solutions for the time-consistent reinsurance-investment strategy and the corresponding value functions are obtained. Finally , the economic signi cance of the results is analyzed. Numerical calculation is also provided to illustrate the in uence of model parameters on optimal strategies.

关 键 词：Poisson-Geometric模型 时间一致 投资 再保险 随机控制 

分 类 号：F830[经济管理—金融学] O211[理学—概率论与数理统计]