| For the insurance companies which conduct the non-life products, the loss reserves are their biggest liabilities. The accurate calculation, effective examination and rational estimate not only make the pricing of the products true and increase the competitive capabilities in the market, but also increase the abilities to pay a debt. And the outstanding claim reserves are the most important part of the reserve. So it is essential to choose a suitable method to estimate the outstanding claim reserves.Now some deterministic methods, especially the chain-ladder, attract much popularity to the insurance companies. The deterministic methods are simple to implement, but they only give a estimate and could not examine the estimate so that it could reach the require of the dynamic financial analysis for the insurance companies. So it is a progress to use a stochastic method for reserve instead of the deterministic method. In order to make use of the expert opinion to increase the precision of the prediction, Bayesian theory and method is used for the reserve.In this paper, we first introduce some common methods for reserve. Next, some theories and method about Bayesian statistical inference are elaborated. On the basis of them, we explain how to establish a Bayesian model which incorporates some expert opinions using Bayesian theory and WinBUGS software. By comparing the result of the Bayesian model with the results from the chain-ladder and B-F method, we have the conclusion that the result from the Bayesian model is directly relative to related to the prior variance of the ultimate losses .The result from the chain-ladder method could be reproduced using the large variance .while the result from the B-F method could be reproduced using the small variance.It is clear that besides the estimate of the reserves, the prediction error and prediction distribution which could be used to evaluate the risk of the reserving could be obtained. |
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