破产时刻和破产赤字对保险公司破产概率的影响研究——基于Erlang风险模型  

Study the Influence of Time to Ruin and Deficit at Ruin on Insurance Company Based on Erlang Risk Model

作　　者：杨利平 周纹心 YANG Liping;ZHOU Wenxin(School of Mathematical Sciences,Chongqing University,Chongqing 401331,China;Shool of Financial Department,Chongqing Normal University,Chongqing 401331,China)

机构地区：[1]重庆大学数学与统计学院,重庆401331 [2]重庆师范大学财务处,重庆401331

出　　处：《重庆师范大学学报（自然科学版）》2019年第3期91-97,共7页Journal of Chongqing Normal University:Natural Science

基　　金：重庆市自然科学基金(No.cstc2016jcyjA0836);重庆市社会科学规划培育项目(No.2018PY69)

摘　　要：【目的】保险公司作为市场经济中重要活动主体,优胜劣汰是自由经济运行的必然结果,为了了解保险公司的生存现状,研究了当初始盈余值大于0时,个人索赔额服从Erlang(3)分布,索赔时间间隔服从Erlang(2)分布的Sparre Andersen风险模型。【方法】通过期望折现罚金函数,运用拉格朗日隐函数定理和拉普拉斯变换的技巧进行求解。【结果】得到破产时间和破产赤字的联合概率密度函数。【结论】根据中国上市保险公司的实际数据,对中国保险公司破产概率进行了实证研究,并证明该模型是有效的。[Purposes]Although insurance companies play an important role in market economy,survival of the fittest is the inevitable result of free economy.In order to understand the real situation of insurance company survival,it studies the Sparre Andersen risk model with the individual claim amount obeying Erlang(3)distribution and the claim time interval obeying Erlang(2)distribution when the initial surplus value is greater than zero.[Methods]Applying the expected discounted penalty function.[Findings]The join density of time to ruin and the deficit at ruin is obtained by using Lagrange implicit function theorem and the Laplace transform.[Conclusions]Finally,according to the actual data of Chinese listed insurance companies,an empirical study on the ruin probability of Chinese insurance companies is carried out,and the model is proved to be effective.

关 键 词：破产时刻 破产赤字 ERLANG分布 

分 类 号：O213.9[理学—概率论与数理统计] O211.3[理学—数学]