带干扰的多复合风险模型的盈余首达给定水平的时间分析  

Analysis of the Time When the Surplus Reaches a Level Firstly in the Multiple-Insurance Risk Model by Diffusion

作　　者：高明美[1,2] 刘喜华[3] 官琳琳[4] 

机构地区：[1]青岛大学数学与统计学院,山东青岛266071 [2]山东省应用数学研究所,山东青岛266071 [3]青岛大学经济学院,山东青岛266071 [4]南京信息工程大学滨江学院,江苏南京210044

出　　处：《数学的实践与认识》2016年第18期32-36,共5页Mathematics in Practice and Theory

基　　金：国家自然科学基金(71273148;71571108);山东省自然科学基金(ZR2014AM019)

摘　　要：对保费收入是复合Poisson过程、理赔含有多个相关险种的带干扰的风险模型盈余首达时间进行研究.首先,对新模型的性质进行了讨论,得到其盈利过程的平稳增量性;其次,基于鞅理论,对风险模型下盈余首次达到给定水平的时间进行了研究.最后,得到了首达时刻的矩母函数以及相应的期望、二阶和三阶中心矩的解析表达式.In view of the classical compound Poisson risk model, we take into account the influence of premium income and more coverage claim to insurance company surplus, a new and practical risk model is proposed to extend the classical compound Poisson risk model. After analyzing the proposed model, the stationary-increment properties of profit process are obtained. By using the martingale method, the time when the surplus reaches a given level for the first time is discussed, and a very simple mathematical expression of its moment generating function and its expect and the kth Central moments （k=1,2,3） are obtained.

关 键 词：风险模型 盈余 停时 鞅 

分 类 号：F224[经济管理—国民经济] F840.4