谱正Lévy过程及其在风险理论中的应用  

Spectrally Positive Levy Processes With Applications in Risk Theory

作　　者：李学堃[1] 陈春敏[2] 张春生[2] 

机构地区：[1]天津工业大学理学院数学系,天津300160 [2]南开大学数学科学学院,天津300071

出　　处：《南开大学学报（自然科学版）》2005年第2期37-41,共5页Acta Scientiarum Naturalium Universitatis Nankaiensis

基　　金：国家自然科学基金资助项目(10271062)

摘　　要：在古典风险模型中,当初始准备金充分大,并且索赔额分布为轻尾形式,破产概率的渐进行为满足指数形式Ce-Ru,C为某个常数,R为某个方程的根.本文研究了推广的风险模型,包括:带干扰的复合Posisson模型,带干扰的Gamma风险模型,带干扰的逆Gaussian风险模型.由于这三类模型均为Lévy过程,跳点仅由索赔引起.我们应用谱正Lévy过程的性质对其研究,证明了这三类风险模型同古典风险模型一样,破产概率的极限行为也满足指数形式.In the classical model of collective risk theory, it is known that the Cramer-Lundberge approximation of the ruin probability has the type Ce-Ru, In this paper, the classical model of collective risk theory is extended to three perturbed risk models: the compound Poisson process perturbed by diffusion, the Gamma process perturbed by diffusion and the Inverse Gausian process perturbed by diffusion. Using the property of the spectrally positive Levy processes, it is proved that the Cramer-Lundberg approximation of the ruin probabilities of the perturbed risk models has a type of exponential the same as the classical model.

关 键 词：谱正Lévy过程 Laplace指数 破产概率 Cramér Lundberg近似 

分 类 号：O2119[理学—概率论与数理统计] F840[理学—数学]