修正的复合Poisson-Geometric风险模型的精算量研究

发布时间：2018-03-31 06:06

本文选题：生存概率　切入点：预警区　出处：《延安大学》2017年硕士论文

【摘要】：结合当前金融保险行业实际,考虑到再投资、随机干扰及保费的收取为复合过程,同时考虑到在保险事务中,风险事件和理赔事件有可能不等价的事实,特别是保险公司推出免赔额和无赔款折扣等制度.现对毛泽春等提出的复合Poisson-Geometric风险模型做进一步推广,使其更接近保险公司的实际经营运作,并对修正的复合风险模型的精算量进行研究.全文的主要研究成果如下:首先,建立保费收入服从复合负二项分布,理赔服从复合Poisson-Geometric过程的带投资的干扰风险模型.通过对盈余过程性质的研究,得到了最终破产概率公式和破产概率上界的Lundberg不等式.以及利用鞅知识对其盈余首次达到给定水平的时刻进行研究,得到了给定水平时刻的拉氏变换以及相应的期望、方差和3阶中心矩的具体表达式.其次,在第三章风险模型的基础上,假设保费收入服从复合Poisson过程.利用全期望公式对修正的复合Poisson-Geometric风险模型的生存概率、Gerber-Shiu折现惩罚函数以及预警区问题进行研究,推导出了所满足的积分微分方程.最后,在第四章建立的风险模型的基础上,引入红利边界.利用全期望公式和盈余过程的马氏性,得到了直至破产时总红利现值的期望、矩母函数及其n阶矩所满足的积分微分方程.
[Abstract]:Considering the reality of the current financial and insurance industry, considering that reinvestment, random interference and premium collection are composite processes, and considering the fact that risk events and claims events may not be equivalent in insurance affairs, In particular, insurance companies have introduced deductible and non-indemnity discount systems. Now the composite Poisson-Geometric risk model proposed by Mao Zechun and others has been further extended to make it closer to the actual operation of the insurance company. The main results of this paper are as follows: firstly, the negative binomial distribution of premium income is established. Compensation claims from the composite Poisson-Geometric process with the investment risk model. Through the study of the nature of the earnings process, The final ruin probability formula and the Lundberg inequality of the upper bound of the ruin probability are obtained. The Lagrangian transformation at the given level and the corresponding expectation are obtained by using martingale knowledge to study the moment at which the surplus reaches a given level for the first time. The concrete expressions of variance and third-order central moments. Secondly, on the basis of the risk model in Chapter 3, Assuming that premium income is derived from the compound Poisson process, the survival probability of the modified compound Poisson-Geometric risk model is studied by using the full expectation formula and the problem of the discounted penalty function of Gerber-Shiu and the early warning area is studied. Finally, the satisfied integrodifferential equation is derived. On the basis of the risk model established in Chapter 4, the dividend boundary is introduced. By using the full expectation formula and the Markov property of the surplus process, the expectation of the present value of the total dividend, the moment generating function and its n-order moments are obtained.
【学位授予单位】：延安大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O211.67

【参考文献】