Poisson-Geometric模型下时间一致的最优再保险-投资策略选择

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.

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

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.