The Prediction Error Of Reserve In Mack Method

China insurance industry is developing rapidly now. For insurance company, the prosperity of the financial market and open environment not only provides a good opportunity, but also puts forward a serious challenge. With the improvement of China insurance institution, reserve gradually becomes more important to insurance company and insurance regulator.For insurance company with non-life insurance business, non-life insurance reserve is the biggest liability and has a direct effect on solvency and financial condition. And outstanding loss reserve evaluation is the characteristics of non-life itself of the decision. There is always difference between estimated outstanding loss reserve and actual outstanding loss reserve for the stochastic and complexity of outstanding claim distribution. And it's helpful to improve the reliability of reserve estimate and perfect the risk control of insurance company that predicting and evaluating the difference scientifically.Now insurance company mainly adopts the chain ladder method and other certainty models to estimate outstanding loss reserve. The chain ladder method which is easy to understand and to apply is suitable for practice of reserve estimation. But the traditional chain ladder method which only has the point estimation of reserve cannot fully reflect the randomness and statistics of data. Though random model can do well in data randomness procession, it's hard for random model to be applied in practice. The Mack method which is a good amalgamation of the advantages of chain ladder method and random model, proposes three basic assumptions on the basis of the chain ladder method, so that the chain ladder also has the statistical properties of random model, like hypothesis testing, interval estimation and prediction error. What's more is that the Mack method doesn't change the advantage of the chain ladder method that easy to understand and to apply.It's discussed how to estimate the prediction error of the outstanding loss reserve estimate on the basis of the Mack method in this paper. First, it's summarized the principle and characteristic of the chain ladder method. Then it's presented the basic assumptions and properties of the Mack method and demonstrated the parameter estimation under the Mack method and the unbiasedness and optimality of the chain ladder method. And then it establishes the model of prediction error of reserve estimate which is compared with the prediction error of other random models as well, to bring about the conclusion that the chain ladder method based on the Mack method is not worse than general random models in estimated accuracy. Finally, it's showed how to extend Mack method to build model of the prediction error of reserve estimate for two correlated run-off triangles.