几类连续时间风险过程破产概率的Lundberg型上界估计

发布时间：2018-06-07 12:23

本文选题：复合Poisson风险模型 + 随机扰动　；参考：《辽宁师范大学》2013年硕士论文

【摘要】：在精算文献中，复合Poisson模型是研究得最广泛的一类更新风险过程。目前，复合Poisson模型有各种推广形式，，其中复合复合Poisson模型（简记为CCPM）由Minkova（Compound Compound Poisson Risk Model. Serdica Mathematical Journal,35,301-310,2009）最早提出，并研究了该模型的相关破产问题和再保险问题。受上述文献启发，本文研究几类广义的CCPM模型，并对这些模型的破产概率进行深入研究。在第一章中，我们介绍了经典的复合Poisson模型和CCPM的相关结果，并且回顾了鞅及布朗运动的相关概念。第二章我们讨论的是保费收入为复合Poisson过程的CCPM的破产概率。首先，介绍了假设的合理性，对各个变量赋予相应的实际意义。然后我们得到了最终破产概率(u)的表达形式，并且给出了一个具体实例。第三章是在第二章的基础上讨论了保费收入为复合Poisson过程带扰动的CCPM。首先，介绍了模型的结构，最终获得破产概率满足的Lundberg型不等式。第四章为了更加贴近保险实践，讨论的是保费收入为双复合Poisson过程的CCPM的破产概率。第五章我们考虑对模型进行更加深入的拓广，即假设保费收入为广义复合复合Poisson过程的CCPM的破产概率。在本文的证明过程中，共分三个步骤完成这几类风险模型所满足的Lundberg型不等式。第一步，保证保险公司有正的安全负载。第二步，对于每种风险模型的盈利过程{S t,t0},我们有E(e rSt) e (r)t,分别求出(r)在不同的模型中表达式，继而验证调节系数的存在性。第三步，利用鞅技巧获得破产概率的上界估计。
[Abstract]:In actuarial literature, compound Poisson model is the most widely studied renewal risk process. At present, the compound Poisson model has various forms of generalization, in which the compound Poisson model (abbreviated as CCPM) is composed of Minkova(Compound Compound Poisson Risk Model.. Serdica Mathematical Journal 35301-310 / 2009 was first put forward, and the related bankruptcy and reinsurance problems of the model were studied. Inspired by the above literatures, this paper studies several generalized CCPM models, and studies the ruin probability of these models. In the first chapter, we introduce the classical composite Poisson model and the related results of CCPM, and review the concepts of martingale and Brownian motion. In chapter 2, we discuss the ruin probability of CCPM in which the premium income is a compound Poisson process. Firstly, the rationality of the hypothesis is introduced, and the corresponding practical significance is given to each variable. Then we obtain the expression of the final ruin probability and give a concrete example. In the third chapter, based on the second chapter, we discuss that the premium income is a complex Poisson process with perturbed CCPM. Firstly, the structure of the model is introduced and the Lundberg type inequality satisfying the ruin probability is obtained. In chapter 4, in order to get closer to the practice of insurance, we discuss the ruin probability of CCPM in which the premium income is a double compound Poisson process. In chapter 5, we consider the further extension of the model, that is, the ruin probability of CCPM assuming that the premium income is a generalized composite Poisson process. In the process of proof in this paper, the Lundberg type inequality satisfied by these risk models is completed in three steps. The first step is to ensure that the insurance company has a positive safety load. In the second step, for the profit process {S t t 0} of each risk model, we have the e rSt. e rSte / rt, respectively, and find out the expressions of r) in different models, and then verify the existence of the adjustment coefficient. In the third step, the upper bound estimate of ruin probability is obtained by using martingale technique.
【学位授予单位】：辽宁师范大学
【学位级别】：硕士
【学位授予年份】：2013
【分类号】：F840.4;F224

【参考文献】