Ruin Probabilities under a Markovian Risk Model  

作　　者：Han-xingWang Da-fanFang Mao-ningTang 

机构地区：[1]DepartmentofMathematicsandInformationScience,ChangshaUniversity,Changsha410003,China [2]DepartmentofMathematics,ShanghaiUniversity,Shanghai200436,China

出　　处：《Acta Mathematicae Applicatae Sinica》2003年第4期621-630,共10页应用数学学报（英文版）

基　　金：Supported by the National Natural Science Foundation of China (No.19971072).

摘　　要：In this paper, a Markovian risk model is developed, in which the occurrence of the claims is described by a point process {N(t)} <SUB>t&#8805;0</SUB> with N(t) being the number of jumps of a Markov chain during the interval [0, t]. For the model, the explicit form of the ruin probability &#936;(0) and the bound for the convergence rate of the ruin probability &#936;(u) are given by using the generalized renewal technique developed in this paper. Finally, we prove that the ruin probability &#936;(u) is a linear combination of some negative exponential functions in a special case when the claims are exponentially distributed and the Markov chain has an intensity matrix (q <SUB>ij </SUB>)<SUB> i,j&#8712;E</SUB> such that q <SUB>m </SUB>= q <SUB>m1</SUB> and q <SUB>i </SUB>= q <SUB>i(i+1)</SUB>, 1 &#8804; i &#8804; m&#8722;1.In this paper, a Markovian risk model is developed, in which the occurrence of the claims is described by a point process {N(t)} <SUB>t&#8805;0</SUB> with N(t) being the number of jumps of a Markov chain during the interval [0, t]. For the model, the explicit form of the ruin probability &#936;(0) and the bound for the convergence rate of the ruin probability &#936;(u) are given by using the generalized renewal technique developed in this paper. Finally, we prove that the ruin probability &#936;(u) is a linear combination of some negative exponential functions in a special case when the claims are exponentially distributed and the Markov chain has an intensity matrix (q <SUB>ij </SUB>)<SUB> i,j&#8712;E</SUB> such that q <SUB>m </SUB>= q <SUB>m1</SUB> and q <SUB>i </SUB>= q <SUB>i(i+1)</SUB>, 1 &#8804; i &#8804; m&#8722;1.

关 键 词：Risk processes ruin probabilities Markov chains 

分 类 号：O211.62[理学—概率论与数理统计]