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≥0</SUB> with N(t) being the number of jumps of a Markov cha...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≥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 Ψ(0) and the bound for the convergence rate of the ruin probability Ψ(u) are given by using the generalized renewal technique developed in this paper. Finally, we prove that the ruin probability Ψ(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∈E</SUB> such that q <SUB>m </SUB>= q <SUB>m1</SUB> and q <SUB>i </SUB>= q <SUB>i(i+1)</SUB>, 1 ≤ i ≤ m−1.展开更多
基金Supported by the National Natural Science Foundation of China (No.19971072).
文摘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≥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 Ψ(0) and the bound for the convergence rate of the ruin probability Ψ(u) are given by using the generalized renewal technique developed in this paper. Finally, we prove that the ruin probability Ψ(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∈E</SUB> such that q <SUB>m </SUB>= q <SUB>m1</SUB> and q <SUB>i </SUB>= q <SUB>i(i+1)</SUB>, 1 ≤ i ≤ m−1.
