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.
作者
杨鹏
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)
出处
《应用数学》
CSCD
北大核心
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)
