| Lvy运动干扰的经典风险模型的Gerber-Shiu函数 |
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| 引用本文： | 陈进源,孔新兵,李泽慧.Lvy运动干扰的经典风险模型的Gerber-Shiu函数[J].数学学报,2012(2):259-272. |
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| 作者姓名： | 陈进源 孔新兵 李泽慧 |
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| 作者单位： | 兰州大学数学与统计学院 |
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| 基金项目： | 国家自然科学基金(10871086);兰州大学中央高校基本科研业务费专项资金(lzujbky-2011-123) |
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| 摘 要： | 通过一个弱收敛方法,本文首次以拉普拉斯变换的形式给出α-稳定Levy运动干扰的经典风险模型的Gerber-Shiu期望折扣惩罚函数(G-S函数).用同样的方法,也获得了这个风险模型的最终破产概率作为本文结果的补充.作为检验,这个风险过程的最终破产概率实际上是G-S函数的特殊情形.
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| 关 键 词： | 复合泊松过程 α-稳定Levy运动 破产概率Gerber-Shiu期望折扣惩罚函数 Skorohod拓扑 |
The Gerber-Shiu Function for a Risk Model Perturbed by Stable Lvy Motion |
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| Jin Yuan CHEN Xin Bing KONG Ze Hui LI.The Gerber-Shiu Function for a Risk Model Perturbed by Stable Lvy Motion[J].Acta Mathematica Sinica,2012(2):259-272. |
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| Authors: | Jin Yuan CHEN Xin Bing KONG Ze Hui LI |
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| Institution: | Jin Yuan CHEN Xin Bing KONG Ze Hui LI School of Mathematics and Statistics,Lanzhou University,Lanzhou 730000,P.R.China |
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| Abstract: | By following a weak convergence approach,the present paper for the first time gives the representation of the Gerber-Shiu expected discounted penalty function (the G-S function) of the risk process perturbed by an a-stable Levy motion in terms of the Laplace transform.Using the same method,this paper also gives the ultimate ruin probability as a byproduct of our results.As a check,we find that the ultimate ruin probability of the risk process is indeed a special case of the G-S function. |
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| Keywords: | compound Poisson process α-stable Levy motion ruin probability Gerber-Shiu expected discounted penalty function Skorohod topology |
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