【作者】 孙旭春；

【导师】 尹传存；

【作者基本信息】 曲阜师范大学 ， 概率论与数理统计， 2008， 硕士

【摘要】 近几年来,Levy风险模型引起了许多学者的兴趣。本文继续研究这一模型。本文的第二章,研究了一个由subordinator驱动且带干扰的风险模型,得到了其破产概率的一个渐近表达式。在第三、四章中,我们研究了两个具有双险种风险模型。根据内容本文分为以下四章:第一章:在本章中,首先我们介绍了风险模型的一些经典结论及其发展情况。接着介绍了本文所要研究的主要问题和所讨论的各种模型。第二章:在第二章中,我们讨论了一类由subordinator驱动且带干扰的Levy风险过程,得到了当索赔量为重尾分布时,它的破产概率渐近表达式。第三章:本章,我们推广了Liand Lu[36]的风险模型,研究了一个具有双险种的风险模型,此风险模型的索赔计数过程分别是Poisson过程和广义Erlang(n)过程。给出了此模型的Gerber-Shiu函数所满足的积分-微分方程组,并给出了它的Laplace变换的一个表达式。当广义Erlang(n)过程为广义Erlang(2)过程时,我们得到了Gerber-Shiu。函数所满足的更新方程。第四章:在本章中,我们考虑了一类带有固定分红策略的双险种风险过程,得到了其分红总量折现期望和分红总量的矩母函数满足的积分-微分方程及其边值条件,并研究了索赔量服从指数分布时上述积分-微分方程的解。更多还原

【Abstract】 More and more people are interested in Levy risk processes, recently. In this paper we go on to study this model. In Chapter 2 of this thesis, we study the ruin probability of a risk model driven by a subordinator and perturbed by a Brownian motion, and give a asymptotic behavior of ruin probability. In Chapters 3-4, we consider two risk models with two class of claims.The thesis is divided into four chapters according to contents:Chapter 1: In this chapter, firstly, we introduce the classical theory of risk models and the development of risk models. Secondly, we introduce the maim problems which are studied and the risk modles which are considered in this thesis.Chapter 2: In this chapter, we consider a risk model driven by a subordinator and perturbed by a Brownian motion, and get some asymptotic expression of ruin probability when the claim sizes have a heavy-tailed distribution.Chapter 3: In this chapter, we consider a risk model involving two independent class of calim processes, that is, we assume the two claim number processes are independent Poisson and generalized Erlang(n) processes, respectively. We give an integro-differential equations system which is satisfied by the Gerber-Shiu function and the expression of the Laplace transform of the Gerber-Shiu functions is obtained. In the last section of this chapter, when the generalized Erlang(n) processes is the generalized Erlang(2) processes, we obtain some generalized renewal equations which are satisfied by the Laplace transforms for the Gerber-Shiu functions.Chapter 4: In this chapter, we consider a risk model involving two independent class of insurance risks with fixed dividend strategy. We get the integro-differential equation for the moment generating function of total dividend discount expectations. We consider the solution of the integro-differential equation when the claim sizes have exponential distribution.更多还原