Generalized Linear Mixed Models For Loss Reserving

As an item of debts, loss reserve plays an important role in safegarding a casualty insurance company’s solvency, profitability and product price.Numerous approaches have been developed to give reasonable estimation-s. They can be divided into two categories, the deterministic models and the stochastic models. The deterministic models including chain ladder method, payments per claim finalized method etc, are simple and easy to operate. How-ever, they have some limitations. For example, some demand compensation modes remain unchanged in all of the developed years. This will ignore some important information such as the random fluctuation etc. The deterministic models performance better in these areas. Generalized linear models (GLM-s) are becoming popular statistical analysis method to estimate loss reserve. Generalized linear mixed models (GLMMs) extend GLMS by including random effects in the linear predictor, and removing the independence assumption.This paper focus on GLMMS to estimate loss reserve under the situation of business classification. The random effects not only determine the correlation structure between observations on the same subject, but also take account of heterogeneity among subjects, due to unobserved characteristics.The paper is divided into six chapters and is structured as follow.Chapter one and two introduce the background, significant and some de-terministic methods of loss reserve.Chapter three first recalls the basic concepts of GLMS. Afterwards GLMM-S are introduced and some maximum likelihood methods are discussed.Chapter four and five, the main chapters of the paper, will sketch the mod-els and provide an example illustrating how GLMMS can be used to estimate the data under the situation of business classification. Draw the conclusion: (1) The fitting effect of the former is superior to the latter; (2) In the classifi-cation of business situations, the result of the former is greater than the latter; (3) Through sensitivity analysis and comparison, the former can reduce the effects of individual abnormal data, the result is more stable and reliable.The last chapter concludes.