改进后的复合Poisson-Geometric风险模型Gerber-Shiu折现惩罚函数  

THE GERBER-SHIU DISCOUNTED PENALTY FUNCTION OF AN IMPROVED POISSON-GEOMETRIC RISK MODEL

作　　者：乔克林[1] 韩建勤[1] QIAO Kelin HAN Jianqin(School of Mathematics and Computer Science, Yan＇an University, Yan＇an 716000)

机构地区：[1]延安大学数学与计算机科学学院,延安716000

出　　处：《系统科学与数学》2016年第10期1743-1752,共10页Journal of Systems Science and Mathematical Sciences

基　　金：陕西省教育厅专项科研计划项目(2013JK0576);延安市科学技术研究发展计划项目(2014ZC-6);延安大学研究生教育创新计划项目(YCX201610)资助课题

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,文章对复合Poisson-Geometric风险模型做进一步推广,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,针对该风险模型,应用全期望公式,推导了Gerber-Shiu折现惩罚函数满足的更新方程,进而得到了在破产时盈余惩罚期望,破产赤字和破产概率满足的更新方程.并以保费额和索赔额均服从指数分布为例,给出破产概率满足的微分方程.以及通过数值例子,分析了初始准备金额,投资金额及保费额等对保险公司最终破产概率的影响.结论为经营者或决策者对各种金融或保险风险进行定量分析和预测提供了理论依据.In this paper, we taken 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 extended the risk model with compound Poisson-Geometric process, defined the investment risk model with interference in which the premiumincome follows the compound Poisson process and the claim numbers follow a com- pound Poisson-Geometric process. Defective renewal equation of the Gerber-Shiu discounted penalty function was given by the method of total expectation formula. Through the above result the defective renewal equation about the ruin probabil- ity and the marginal distributions of the deficit at ruin were deduced. At last, an example was given that the premium amounts and claim amounts follow exponen- tial distribution, and the differential equation for the ruin probability was derived. Meanwhile, the effects of the initial amount of preparation, the amount of investment, the amount of insurance premium and ect on the final ruin probability of insurance companies were analyzed by a numerical example. Objective to provide a theoretical basis for managers or decision makers to make quantitative analysis and prediction of the financial or insurance risk.

关 键 词：POISSON过程 Poisson—Geometric过程 更新方程 破产概率 

分 类 号：F840[经济管理—保险] F224