| Survival probability and ruin probability of a risk model |
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| 作者单位： | LUO Jian-hua College of Science，Central South University of Forestry and Technology，Changsha 410004，China;Institute of Statistics，Central South University of Forestry and Technology，Changsha 410004，China. |
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| 基金项目： | Acknowledgements. The author would like to thank the anonymous referee for valuable comments and suggestions to improve the earlier version of the paper. He would also like to thank Professor Yang Xiangqun for the detailed and critical comments on an earlier draft of this paper. |
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| 摘 要： | In this paper, a new risk model is studied in which the rate of premium income is regarded as a random variable, the arrival of insurance policies is a Poisson process and the process of claim occurring is p-thinning process. The integral representations of the survival probability are gotten. The explicit formula of the survival probability on the infinite interval is obtained in the special casc cxponential distribution.The Lundberg inequality and the common formula of the ruin probability are gotten in terms of some techniques from martingale theory.
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| 关 键 词： | 存活率 破产概率 风险模型 积分表示 |
Survival probability and ruin probability of a risk model |
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| Authors: | Jian-hua Luo |
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| Institution: | [1]College of Science, Central South University of Forestry and Technology, Changsha 410004, China [2]Institute of Statistics, Central South University of Forestry and Technology, Changsha 410004, China |
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| Abstract: | In this paper, a new risk model is studied in which the rate of premium income is regarded as a random variable, the arrival of insurance policies is a Poisson process and the process of claim occurring is p-thinning process. The integral representations of the survival probability are gotten. The explicit formula of the survival probability on the infinite interval is obtained in the special casc--exponential distribution.The Lundberg inequality and the common formula of the ruin probability are gotten in terms of some techniques from martingale theory. |
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| Keywords: | risk model thinning process survival probability martingale ruin probability integral repre-sentation |
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