摘要
在考虑到因保费收入和通货膨胀等随机干扰的影响,以及将多余资本用于投资来提高赔付能力的基础上,建立以保费收入服从复合Poisson过程,理赔量服从复合Poisson-Geometric过程的带投资的干扰风险模型,然后应用盈余过程的强马氏性和全期望公式,得到了第一个预警区的条件矩母函数满足的微积分方程,及当保费额和索赔额都服从指数分布情形下满足的微分方程。
In this paper,we took into account the effects of random interference because of the premiums＇randomness and inflation in insurance business,and we used the surplus capital to invest in order to enhance the insurance payment level.Based on the points above,we defined the investment risk model with interference in which the premium income follows the compound Poisson process and the claim numbers follows a compound Poisson-Geometric process.By taking full advantage of the strong Markov property of the surplus process and the total expectation formula,a integral differential equation of a conditional moment generating function for the first duration of negative surplus has been obtained.Finally,the differential equation has been given When premium income and claim sizes follow exponential distribution.
出处
《重庆师范大学学报（自然科学版）》
CAS
CSCD
北大核心
2016年第5期58-62,共5页
Journal of Chongqing Normal University:Natural Science
基金
陕西省教育厅专项科研计划项目(No.2013JK0576)
延安市科学技术研究发展计划项目(No.2014ZC-6)
延安大学研究生教育创新计划项目(No.YCX201610)
