带混合保费和投资复合Poisson-Geometric风险模型的生存概率

The Survival Probability of an Poisson-Geometric Risk Model with Mixed Premium and Investment

在考虑到保费收入和通货膨胀等随机因素的干扰以及保险公司将多余资本用于投资来提高其赔付能力的基础上,本文对经典风险模型进行了推广。首先,建立了混合保费收取下带投资和扰动的双复合Poisson-Geometric过程的双险种风险模型,随机保费收入服从复合Poisson过程,理赔过程服从复合Poisson-Geometric过程;其次,应用全期望公式,推导了该模型生存概率的积分微分方程;最后,当保费、理赔过程服从特定指数分布时,得到其满足的微分方程。

Taking into account the disturbance of random factors such as premium income and inflation, as well as the excess capital invested by insurance companies to improve their payability, the classical risk model is extended in this paper.Firstly, a double risk model with investment and perturbation is established under the mixed premium collection. The stochastic premium income follows the compound Poisson process, and the claims process follows the compound Poisson-Geometric process. Secondly, the integral differential equation of the survival probability of the model is derived by using the total expectation formula. Finally, when the premium and claim process obey a specific exponential distribution, the differential equation satisfied is obtained.