| Ruin Probabilities under a Markovian Risk Model |
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| 作者姓名： | Han-xingWang Da-fanFang Mao-ningTang |
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| 作者单位： | [1]DepartmentofMathematicsandInformationScience,ChangshaUniversity,Changsha410003,China [2]DepartmentofMathematics,ShanghaiUniversity,Shanghai200436,China |
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| 基金项目： | Supported by the National Natural Science Foundation of China (No.19971072). |
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| 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)}t≥0 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(qij)i，j∈E such that qm = qml and qi=qi(i 1), 1≤i≤m-1.
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| 关 键 词： | Markovian风险模型 破产概率 Markov链 收敛速率 |
| 收稿时间： | 10 April 2002 |
Ruin Probabilities under a Markovian
Risk Model |
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| Han-xingWang Da-fanFang Mao-ningTang.Ruin Probabilities under a Markovian Risk Model[J].Acta Mathematicae Applicatae Sinica,2003,19(4):621-630. |
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| Authors: | Email author" target="_blank">Han-xing?WangEmail author Da-fan?Fang Mao-ning?Tang |
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| Institution: | (1) Department of Mathematics and Information Science, Changsha University, Changsha, 410003, China;(2) Department of Mathematics, Shanghai University, Shanghai, 200436, China |
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| Abstract: | Abstract
In this paper, a Markovian risk model is developed, in
which the occurrence of the claims is described by a point
process {N(t)}
t 0
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  (0) and the bound for the
convergence rate of the ruin probability (u) are given by using the generalized
renewal technique developed in this paper. Finally, we prove
that the ruin probability (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
ij
)
i,j E such that
q
m
= q
m1 and
q
i
= q
i(i+1), 1 
i m–1.Supported by the National Natural Science Foundation
of China (No. 19971072). |
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| Keywords: | Risk processes ruin probabilities Markov chains |
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