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相依索赔的二项风险模型的Gerber-shiu贴现罚函数
引用本文:刘东海,刘再明,龚日朝.相依索赔的二项风险模型的Gerber-shiu贴现罚函数[J].经济数学,2012,29(2):35-39.
作者姓名:刘东海  刘再明  龚日朝
作者单位:1. 湖南科技大学,数学与计算科学学院,湖南湘潭411201;中南大学,数学与统计学院,湖南长沙410004
2. 湖南科技大学,数学与计算科学学院,湖南湘潭411201
3. 湖南科技大学,商学院,湖南湘潭411201
基金项目:教育部人文社会科学青年基金,国家社会科学基金
摘    要:研究一类索赔时间相依的二项风险模型,根据索赔额的大小随机产生一副索赔.通过引入辅助模型,运用概率论的分析方法得到了任意初始值μ下的Gerber-Shiu贴现罚函数,并求得了初始值为0时最终破产概率的明确表达式.最后结合保险实务进行了举例.

关 键 词:二项风险模型  相依索赔  副索赔  贴现罚函数

The Gerber-shiu Discounted Penalty Function in the Correlated Binomial Risk Model
LIU Dong-hai,LIU Zai-ming,Gong Ri-zhao.The Gerber-shiu Discounted Penalty Function in the Correlated Binomial Risk Model[J].Mathematics in Economics,2012,29(2):35-39.
Authors:LIU Dong-hai  LIU Zai-ming  Gong Ri-zhao
Institution:1.Department of Mathematics,Hunan University of Science and Technology,Xiangtan,Hunan 411201,China; 2.Department of Mathematics,Central South University,Changsha,Hunan 410075,China; 3.Department of Business,Hunan University of Science and Technology,Xiangtan,Hunan 411201,China)
Abstract:This paper considered the compound binomial model with correlated claims in which every claim can produce a by-claim according to the amount of it.By means of auxiliary model and using the methods of probability,we obtained the Gerber-Shiu Discounted Penalty Function in the correlated binomial risk model.Furthermore,the explicit expression for the probability was given when the initial surplus is zero.Finally,we show some examples according to the insurance case.
Keywords:binomial risk model  correlated claim  by-claim  discount penalty function
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