Stochastic Non-life RBNS Reserve Method Analyst: Beyesian Method

Insurance companies are financial institutions for debt financing. It will measure the future risk in a certain price, and collect in the way of premiums as the liabilities to spread the risk of investors and gain Profit. Therefore, the management of liabilities for insurance companies is very important, it determines the future solvency of insurance companies and profitability. The reserve is the major liabilities of insurance companies. The accuracy and adequacy of assessment of reserve will affect its operating results of the accounting responsibility and the ability to perform insurance payments. Meanwhile, Non-life insurance does not have the same features as life insurance. Period is short, the long tail business and payment delay, so the non-life insurance's assessment of reserve is very complicated, and it is important issues for theory study.Currently, the domestic property insurance company mainly use the deterministic method such as chain ladder method, BF method to extract the outstanding claims re-serves. Deterministic method is simple in principle, easy operation, and can be calculated a specific value under the assumption. But it also has its limitations. This method only gives the point estimate of outstanding loss reserve, the accuracy can not be predicted, and future claims Randomness has not be reflected. Therefore, based on the deterministic model, scholars bring out the concept of stochastic model. Outstanding claims are consid-ered as random variable, and the stochastic model combined with a variety of statistical methods. These are derived based on aggregate data structure model, missing the useful information of individual data. Thus, in order to solve the problem, a stochastic model is considered based on individual data structure.This research is carried out based on individual data, so that data can be applied to the model contained useful individual information. And in practice, the amount of compensation may contain unknown ingredients, we can use Bayesian approach to esti-mate it. As in the individual data, the reserve is able to be separated as reported but not settled yet and none-reported outstanding claims. And in this article we only dis-cuss outstanding claims that have been reported but not settled yet.The ideal goal to estimate reserve is to get it distribution under the conditions of observations, so in the second chapter presents a new model based on individual Bayes method. The core idea of the model is to put the beyesian assumption original on the aggregate data into in-dividual data, and to calculate the individual outstanding claims Distribution under the observation claim data. Finally, we need to calculate the overall conditional distribution of outstanding claims in each accident year. In this concept, we introduce two models under specific distribution assumptions, and obtain the conditional distribution. Once we know the conditional distribution, and we can get other statistical information other than expectation of outstanding claims. The expectations of its conditional variance under the conditional variance is less than aggregate data, indicating that the stability better than the aggregate data. In the third chapter, simulation method is used to calculate a specific numerical solution. Compared with the aggregate model and the chain ladder method, the results tell that the reserve should be extracted is different than CL method, and can't tell which is better than others. Meanwhile, the different assumptions of the distributions and parameters will also affect the results.