摘要
考虑了一类具有阈值安排的风险模型,模型中包含了两类索赔,两类索赔之间存在相依关系。如果第一类索赔的索赔额随机变量的取值大于或者等于阈值随机变量的取值,将引发第二类索赔,并且第二类索赔的发生时间可能延迟。利用微分方程理论,得到了此风险模型生存概率满足的高阶齐次线性微分方程,给出了生存概率(破产概率)的解析表达式,证明了生存概率与索赔延迟发生之间的关系,并且给出了数值结果。
In this paper,a risk model with claim threshold is considered. Two classes of dependent claims are defined in this risk model. The occurrence of the second claim depends on the claim size of the first claim and the threshold level. Moreover,the occurrence of the second claim may be delayed. We give and solve the higher order linear differential equation satisfying by the survival probability. The explicit formulae of survival probabilities are derived. Finally,we illustrate the influence of the model parameters in the risk model on the survival probability by numerical examples.
出处
《南昌工程学院学报》
CAS
2016年第3期32-38,共7页
Journal of Nanchang Institute of Technology
基金
国家自然科学基金资助项目(11561047)
江西省自然科学基金资助项目(20142BAB211015)
江西省教育厅科技项目(GJJ151101
GJJ151116)
国家大学生创新创业项目(2014-12)
关键词
险理论
生存概率
微分方程
risk theory
survival probability
differential equation
