Stochastic Non-life Reserve Method Analyst:Bayesian

Liability reserve for non-life insurance is the main liabilities. Outstanding claim re-serves calculated by a reasonable method can greatly increased the adequacy and accuracy of the reserve, which affect the insurance company much in income calculation and its solvency capacity, the insurance compensation capability. Therefore, the non-life insur-ance's assessment of liability reserve is an important issue not only for the CIRC but also for theory study.Classical methods for reserve assessment such as the chain ladder method, the BF method are all deterministic method based on aggregate data, which are extensively used by the insurance companies due to its advantages of simple in principle and easy operation. However, there also exists many limits, for example, it not only ignores the valid information in the individual data, but also ignores the randomness of the data itself. So we can only get a specific value of the reserve based on this method, but can' t know the accuracy of estimated reserve. Therefore, in recent years, scholars bring out the concept of the stochastic model based on individual data.Chapter3present a model based on individual Bayes method, which is derived from a random reserve study model based on the aggregate proposed by Verral (1998). In this model, we can assume that the claim data comply with a known distribution, and then we can calculate the individual outstanding claims distribution under the observed claim data. Therefore, not only we can get some feature of the reserve such as expectation and variance, but also we can get some other useful statistical information. At the same time, this paper presents two specific models to describe the thought of the model, and get the individual outstanding claims distribution under the observed claim data. In chapter4, simulation method is used to produce the claim data, which is thought as the true claim data. We have respectively calculated the outstanding claims under the two models. Compared with the claims obtained by the chain ladder method and the claims obtained by the individual Bayes method, we can obviously find that claims obtained by the individual Bayes method is more similar to the true claim data, and it is less volatile and more stable.