【作者】 郑丽丽；

【导师】 付俐；

【作者基本信息】 北京交通大学 ， 概率论与数理统计， 2008， 硕士

【摘要】 精算学是将数学方法应用于保险所形成的一套理论体系,是应用数学研究领域和金融保险研究领域这两者之间的一个边缘学科.汽车保险奖惩系统是现代精算学中的一个重要研究课题,是广泛应用于世界各国保险公司的一种经验估费系统,主要是根据投保人索赔记录来确定续期保费.本文主要用马尔可夫链,数理统计理论和最优化方法等来研究汽车保险奖惩系统及其定价,重点是奖惩系统的设计与改进,主要研究内容和成果如下:1.在保险实践中,要求索赔的事故次数比实际发生的事故次数要少,根据这个特点,文中用调零的复合分布类来拟合同质性保单的索赔次数,具体的讨论了该分布类中两种特殊分布,对分布中的参数进行了估计,给出了数值算例,并分析了拟合结果.2.考虑索赔次数的奖惩系统,在最小化保险人损失的目标下构建我国现行汽车保险转移规则下的最优奖惩系统.然后,对有线性约束的路径相关奖惩系统进行研究,通过对等级增加必要的下标使新规则成为马尔可夫链,在线性费率等级的约束下得到最小化保险人损失的线性路径相关最优奖惩系统.3.将索赔金额因素引入奖惩系统,分别在期望值原则,期望-方差原则下构造基于索赔次数和索赔金额的最优奖惩系统,并证明期望值原则下的系统能保持财物平衡.4.构造考虑索赔额大小和应负责任的奖惩系统,建立转移矩阵,并给出了求费率系数的方法.5.从平均自留额水平,瞬时弹性和收敛速度三个方面对我国五大奖惩系统进行实证分析,指出存在的优缺点.为后面的理论研究和保险实践提供参考.更多还原

【Abstract】 Actuarial science applies mathematical methods in insurance and is a science between applied mathematics and insurance. Bonus-malus system of automobile insurance is an important topic in actuarial science.Markov chain, Statistical theory and Optimization method are used to study bonus-malus systems, mainly focusing on revising and designing of the bonus-malus system. The primary research content and results are obtained as followes:1. Based on the characteristic that the claim number which reported is less than the practical accident number in a portfolio of insurance policyholder, the paper presented a new class of claim distribution to fit the claims numbers on homogeneous policyholders. Parameters estimated by maximum likelihood in the two distributions. Finally, we gave a example and analyzed the results.2. We study optimal bonus-malus system in which claim frequency is used as posterior factor. Two optimal four level BMSs with present Chinese BMS’s transfer rule are obtained under two objects, minimize insurer’s expected loss .We also study path-dependent BMS with linear BM coefficients. If transfer rule is related to more than one past periods’ claim record, we can get a new rule by adding a subscript to each BM level. The new rule is a Markov chain, An optimal BMS is obtained to minimum insurer’s expected loss under linear restrict.3. Besides claim number, claim amount is used in BMS. In the BMS, in the BMS considering both claim frequency and claim severity, expected value principle and expected-variance principle are used to build optimal BMS.4. We constructed an applied BMS involving claim amount and responsibility to abate unfair in the BMS in which claim number is considered as only factor.5. We do practical research on BMS, we compare and comment on the Bonus-Malus antomobile insurance systems of five Chinese automobile companies in detail, at the same time point out the lacks.更多还原