The Estimation Of Claim Reserves Under Hierarchical Generalized Linear Models

As an important insurance companies'liability, the adequacy of Claim Reserves extraction directly affects the companies'solvency, therefore many insurance companies and regulators attach great importance to it. With the development of statistics and computer technology, stochastic simulation method was introduced into the Claims Reserve extraction. For example, GLMs (Generalized Linear Models) are one of the most widely used stochastic models,which require each observed value of response variable to be mutually independent and obey the exponential family distribution. According to the insurance companies'claims record, the loss of an accident year in different development years belongs to the results of repeated observations for the same goal. Apparently they are not mutually independent and are in line with the characteristics of longitudinal data. In this case, there is no guarantee that the incremental compensation or the accumulated compensation of the same accident year in different development years is independent of each other. Consequently, the result of extracting Claim Reserves by building GLMs would cause deviation because of the influence of independence.With the introduction of HGLMs (Hierarchical Generalized linear Models), this thesis focused on the characteristics of Claims Reserve when serving as longitudinal data. On the basis of GLMs, random effects were introduced into HGLMs. Random effects could respond the longitudinal characteristics of repeated observation data of same accident year in different development years. Meanwhile, by making use of the external information, it could take the heterogeneity which caused by the characteristics that hadn't been observed in different accident years into consideration.As a result, in the empirical part of this thesis, the Claim Reserves assessment results and deterministic method of HGLMs were compared with assessment results of Bayesian Generalized Linear Models under different shape parameter conditions, and the predicted MSE (mean square error) was also compared.According to the empirical results, Claim Reserves results obtained by applying HGLMs and the results obtained from Bayesian optimal estimation when the MESP and shape parameters were 100 were very close, suggesting that Claim Reserves assessment results of HGLMs were credible. And the priori weights could be adjusted according to the priori information and experience compensation, overcoming the condition that Claims Reserve assessment results could be influenced by setting the shape parameter subjectively in Bayesian Generalized Linear Models. In addition, in order to investigate the applicability of HGLMs in Claims Reserve assessment, this thesis analyzed the changing situations of Claim Reserves assessment results on the basis of Chain Ladder method, Bayesian Generalized Linear Models and HGLMs respectively when the insurance company had emergency situations, so that to illustrate that in the case of emergency situations, HGLMs could get more stable Claim Reserves evaluation value.