Applied Mathematics and Mechanics

, Volume 28, Issue 7, pp 955–962

# Markovian risk process

• Wang Han-xing  (王汉兴)
• Yan Yun-zhi  (颜云志)
• Zhao Fei  (赵飞)
• Fang Da-fan  (方大凡)
Article

## Abstract

A Markovian risk process is considered in this paper, which is generalization of the classical risk model. It is proper that a risk process with large claims is modelled as the Markovian risk model. In such a model, the occurrence of claims is described by a point process {N(t)} t≥0 with N(t) being the number of jumps during the interval (0,t] for a Markov jump process. The ruin probability ψ(u) of a company facing such a risk model is mainly studied. An integral equation satisfied by the ruin probability function ψ(u) is obtained and the bounds for the convergence rate of the ruin probability ψ(u) are given by using a generalized renewal technique developed in the paper.

## Key words

risk process ruin probability Markov jump process

O211

62P05 60F10

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© Editorial Committee of Appl. Math. Mech. 2007

## Authors and Affiliations

• Wang Han-xing  (王汉兴)
• 1
• 2
Email author
• Yan Yun-zhi  (颜云志)
• 2
• Zhao Fei  (赵飞)
• 2
• Fang Da-fan  (方大凡)
• 3
1. 1.China Lixin Risk Management Research InstituteShanghai Lixin University of CommerceShanghaiP. R. China
2. 2.Department of MathematicsShanghai UniversityShanghaiP. R. China
3. 3.Department of MathematicsHunan Institute of Science and TechnologyYueyangP. R. China