摘要
为了得到带常利率相依风险模型的风险度量,用概率极限理论及随机过程的方法得到了上述模型有限时破产概率的渐近估计.采用有限时破产概率的加权表达式、加权和的一致渐近性质及相依结构的处理方法研究了索赔额之间的相依性、索赔来到时间间隔的相依性及索赔额的分布对带常利率风险模型的有限时破产概率的影响.结果表明:对于索赔额的分布属于控制变化尾分布族、索赔额之间具有类似渐近独立的相依结构及索赔来到时间间隔具有宽相依结构时,带常利率的风险模型的有限时破产概率呈现出一定的渐近性质,此渐近性质与索赔额的分布、常利率、初始资本及时间范围有关.当考虑的时间范围及索赔量变大时,将增加有限时破产概率的上下界;当常利率及初始资本变大时,将减小有限时破产概率的上下界.但索赔额及索赔来到时间间隔的相依性对有限时破产概率的影响不大.
In order to obtain the risk measure of a dependent risk model with a constant interest rate,the asymptotic estimates of the finite-time ruin probability are obtained for the above model by using the probability limiting theory and stochastic process.Applying the weighted formula of the finite-time ruin probability,the uniform asymptotics of the weight sums and the way dealing with the dependence structures,the effects of the dependence of the claim sizes,the dependence of the inter-arrival times and the distribution of the claim sizes on the finite-time ruin probability of the risk model with a constant interest rate are investigated.The obtained results show that when the claim sizes have a dominated varying-tailed distribution and a dependence structure similar to the asymptotic independence and the inter-arrival times have a wide dependence structure,the finite-time ruin probability of the risk model with a constant interest rate has some asymptotic properties.These asymptotics have relations with the distribution of the claim sizes,the constant interest rate,the initial capital,and the time range.With the increase in the time range and the claim sizes,the upper and lower bounds of the finite-time ruin probability will increase;with the increase in the constant interest rate and the initial capital,the upper and lower bounds of the finite-time ruin probability will decrease.However,the dependence structures of the claim sizes and the inter-arrival times have little effect on the finite-time ruin probability.
出处
《东南大学学报（自然科学版）》
EI
CAS
CSCD
北大核心
2012年第6期1243-1248,共6页
Journal of Southeast University：Natural Science Edition
基金
国家自然科学基金资助项目(11071182
11171065)
国家自然科学基金数学天元基金资助项目(11226211)
江苏省自然科学基金资助项目(BK2012165
BK2011058)
中国博士后科学基金资助项目(2012M520963)
苏州科技学院院科研基金资助项目
关键词
相依风险模型
有限时破产概率
控制变化尾
渐近性
dependent risk model
finite-time ruin probability
dominated varying tail
asymptotics
