基于有限服务排队系统的未决赔款准备金分布

若保险赔付工作中赔付人员有限,根据服务人员有限的排队系统的性质,可以研究保险公司所需计提的未决赔款准备金的分布函数.当假设赔付服务工作人员为c个,使用M/M/c/∞和G/M/c/∞排队系统的性质可以得到未决赔款准备金分布函数和年末所需增加计提的未决赔款准备金的分布及其界值.当假设赔付服务工作人员仅一个,使用M/G/1/∞排队系统的性质可以得到此时未决赔款准备金的分布函数.并且在假设损失赔付额取正整数的条件下,得到年末保险公司所需增加计提的未决赔款准备金分布的递推公式.而且通过计算实例表明结论的实用性,及所得到的递推公式在以往难以准确求解未决赔款准备金分布时是十分有效的.

The Outstanding Claims Reserve by Queueing System with Limited Server

In this paper we present the Outstanding Claims Reserve method which is based on the queueing model with limited server.First,we state a stochastic claims reserving model suffices to the supposition of /G/1/∞queueing model.The stochastic claims reserving model produce estimates not only of the expected value and the variation,but also of the distribution function about the Outstanding Claims Rreserve.When the number of server is arbitrary constant we explore two types of Stochastic claims reserving model suffices to the supposition of M/M/c/∞and G/M/c/∞Queueing System.Because the expression of the distribution function of the Outstanding Claims Reserve is difficult to gain when the loss distribution is a general distribution,we suppose the claim is a positive integer,and establish stochastic claims reserving model in order to study on the recursion formula of the Outstanding Claims Reserve.Finally,two examples are given for explaining the value and application of these results.