A Study On The Distribution Of The Outstanding Claim Reserver And It's Bounds

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.