Research On Outstanding Claims Reserve Based On GLMM And Empirical Analysis

As an industry operating on liability, one of the most important liabilities of non-life insurance companies is outstanding Claims Reserve. As the decisive factor of the company’s operating condition, outstanding Claims Reserve has been attracting the attention of the insurance regulatory authorities and insurance companies.Currently, there are two methods for estimation of outstanding Claims Reserve, deterministic models and stochastic models. The deterministic models include the traditional chain ladder method, case payment method and B-F method, etc. As a newly-proposed method, study on the stochastic models is relatively not very mature, the focus of which is the generalized linear models(GLMs). On one hand, as a generalization of the linear model in two aspects, the stochastic models can better fit insurance data, while on the other hand it also has its own deficiencies in that it requires independence among random variables,which is too harsh for many actuarial data, for example: spatial data, longitudinal data,clustering data, etc.In this paper, to overcome the insu?ciencies of GLMs, the generalized linear mixed models(GLMMs) will be put forward. Based on GLMs, GLMMs include random e?ects in the linear predictor, which response the heterogeneity among subjects and the correlation between observations on the same subject. Two methods for estimating parameters of GLMMs will be given in this paper, PQL analysis and adaptive G-H integral method.Finally, with R software, this model is applied to process longitudinal data and estimate the outstanding Claims Reserve.