【作者】 刘燕；

【导师】 唐应辉；

【作者基本信息】 电子科技大学 ， 管理科学与工程， 2006， 博士

【摘要】 未决赔款准备金是保险公司主要的负债之一，而且未决赔款准备金的计提水平将直接影响保险公司的盈利、产品定价、偿付能力和税收，所以未决赔款准备金也是非寿险公司必须使用精算方法谨慎评估的项目。使用当前保险实务中常用的未决赔款准备金计提方法，我们仅仅可以得到未决赔款准备金的一个估计值，而不能对未决赔款准备金的分布函数和提存的缺口进行量化的分析。本文基于著名精算学家Goovearts M.J.教授提出的研究未决赔款准备金分布函数的思想，而与Goovaerts M.J.和Verrall教授等使用线形模型和对数正态模型等流量模型的方法不同，从另外一个角度进行分析，将计提未决赔款准备金的风险模型与排队模型相对应，从而建立排队数学模型，在这种新的数学模型中使用排队论分析随机服务系统的方法探讨未决赔款准备金的分布函数，弥补实务中常用的方法不能量化未决赔款准备金的分布和缺口的不足，并且论证了这种使用排队数学模型的方法也可以应用于分析IBNR准备金的分布函数。由于未决赔款准备金分布函数的表达式中含有一次损失赔付额的分布函数的卷积Fⁱ（x），当一次损失赔付额为一般分布时，很难求得Fⁱ（x）的具体表达式，所以本文进一步由一次损失赔付额的分布函数所满足的分布类的性质，研究未决赔款准备金分布的界值和IBNR准备金分布函数的界值。在一次损失赔付额的分布函数为IFR、IFRA、NBUE和HNBUE分布类时，我们分别得到了未决赔款准备金分布函数的界值的表达式。而后通过一次损失赔付额的分布函数为各种分布类的不同情况下的实例分析，给出了未决赔款准备金分布函数的界值的具体值和分布曲线，并且验证了未决赔款准备金分布函数的界值的可行性和有效性。因此，研究得到的有关未决赔款准备金分布函数的界值的结论具有重要的理论意义和应用价值。然后，本文通过使用随机序的性质，在假设损失的发生、损失的报告和赔付服务时间为一般分布时，将损失的发生、损失的报告和赔付服务由随机序关系建立排队数学模型，论证在更广泛的一般到达和一般服务的假设条件下，未决赔款准备金的分布函数的界值和IBNR准备金分布函数的界值。并且通过实例的计算和分析，表明此时得到的未决赔款准备金分布函数界值的有效性和实用价值。最后，本文从保险实务中计提未决赔款准备金的应用角度出发，根据未决赔款准备金的分布函数提出了偿付充足率的概念，对计提未决赔款准备金的充足程度给出了量化的表示方法。而后又由偿付充足率的概念引入了一种新的计提未决赔款准备金的方法——充足率法，并且用实例论证了充足率法的可行性和优越性，分析充足率法在保险公司计提未决赔款准备金的工作中的应用和在保险监管中使用充足率法的优点。更多还原

【Abstract】 Accurate estimation of the level of the Outstanding Claims Reserve for an insurancecompany is required because it is the major liability in insurance company’s balance sheetand it impacts on multiple aspects of the operation of the insurance company: dividenddeclaration, solvency, insurance product pricing and tax payments.By the presently predominant methods, we can only find an estimation of theOutstanding Claims Reserve, and can’t discuss the distribution of the Outstanding ClaimsReserve. Based on the Professor Gooveart M.J.’s idea of researching the distribution of theOutstanding Claims Reserve, from another point of view, we use the analysis method ofqueueing theory and research tools of the distribution class, such as IFR, IFRA, NBUEand HNBUE distribution class. We found a mathematical model by the risk model of theestimation of the Outstanding Claims Reserve corresponding to the queueing model. So inthis mathematical model, we can study on the distribution of the Outstanding ClaimsReserve. Therefore, we can gain some valuable expression of the distribution of theOutstanding Claims Reserve. And in this paper, we prove that the distribution of the IBNRclaims reserve also can be discussed by this mathematical model.When the loss distribution is a general distribution, we know that the values of thedistribution of the Outstanding Claims Reserve are difficult to gain, because it contains theith convolution of the loss distribution. Therefore, we introduce the distribution class ofthe loss distribution for analysis the upper and lower bounds of the distribution of theOutstanding Claims Reserve and the IBNR claims reserve. So we found large numbers ofvaluable bounds of the distribution of the Outstanding Claims Reserve when the lossdistribution is IFR, IFRA, NBUE, or HNBUE distribution class. And some examplesshowed that these results about the upper and lower bounds of the distribution of theOutstanding Claims Reserve in this paper are viable and effectual, and they have veryimportant applied value.Then, considering that the occurrence, reporting and claim of the outstanding claim isthe general distribution, this paper try to use the stochastic order not only on the process ofthe claim’s occurrence, but also on the process of reporting and claim of the outstandingclaim. On the stochastic order, we can found a mathematical model and its correspondingqueueing model. Thereby, we gain some bounds of the distribution of the OutstandingClaims Reserve in wider range.Finally, based on the distribution of the Outstanding Claims Reserve, we introduce the conception of the solvency enough ratio and the enough ratio method, and take anexample to explain its application. Furthermore, this paper analyses how to apply theenough ratio method to the insurance regulation of the Outstanding Claims Reserve, andshows the benefits of using the enough ratio method.更多还原