【作者】 杨文伟；

【导师】 胡泽春；

【作者基本信息】 南京大学 ， 应用数学， 2011， 硕士

【摘要】 这篇论文主要讨论了两类保费速率不为固定常数的含相关性的风险模型。第一类,保费速率由当前盈余决定。当盈余r不大于常数v时,保费速率为c(r)=c1+εr,反之,保费速率为c(r)=c2+εr,其中c1.c2,ε,r均为常数,本文给出了破产概率的表达式,并对索赔过程为指数分布的情形进行了具体计算；第二类,具有半马氏结构相依性的风险模型。该模型中,保费速率,索赔额分布,索赔间隔时间分布均被一离散时间马氏链决定。本文利用拉式变换对该模型的罚金折现函数进行分析,并给出了破产时刻、破产前盈余、破产赤字的任意阶矩的表达式。并以时间间隔分布满足Erlang(n)的模型为例进行了详细的计算。更多还原

【Abstract】 This thesis studies two dependent risk models in which the premium rate is not a fixed constant. The first type is a time-dependent premium risk model in which premium rates are adjusted continuously according to the current level of an insurer’s surplus. When surplus r(?)υ, the premium rate c(r)=c1+εr and when surplus r>υ, the premium rate c(r)=C2+εr, where c1, c2,εand r are all constants. We obtain expression for the ruin probability. For the exponential claim sizes, we exactly solve the ruin probability step-by-step. the second type is a Markov-dependent risk model in which the premium rate, the claim amounts and the interclaim time are depended by an irreducible discrete-time Markov chain. Based on the analysis of the discounted penalty function by means of Laplace-Stieltjes transforms, we drive moments of three characteristics of the ruin process. A renewal model with generalized Erlang(n)-interclaim times is contained as a special case.更多还原