Generalized Linear Mixed Model For Outstanding Claims Reserves

Claims originating in a particular year often can not be finalized in the same financial year. According to the solvency requirement of China Insurance Regulatory Commission, insurance company should calculate the outstanding claim reserve.Traditional claims reserving techniques are based on so-called run-off triangles containing aggregate claim figures. Such a triangle provides a summary of an underlying data set with individual claim figures. The problem of individual reserving is often encountered in the reinsurance business. For these reasons, the contribution of the paper is to present a statistical framework to model data sets containing individual records, which is meaningful.Antonio, Beirlant, Hoedemaker & Verlack(2006) explained how individual record data sets can be modeled in the context of Lognormal mixed models and how these models lead to forecasts for future payments for the individual cases. However, it is important to point out that the logarithm of the individual data is modeled and not the data on the original scale.Inspired by discussions above, the contributions of the paper are modeling the original individual claim data through Generalized Linear Mixed Models and forecasting the future payments for individual cases.The rest of the paper has been organized as follows. Section 2 introduces the traditional claims reserving. Section 3 motivates the use of the generalized linear mixed model and contains the necessary statistical background. Section 4 explains how outstanding claim reserving based on individual record data sets can be performed within the framework of generalized linear mixed models in Bayesian way. Section 5 describes Lognormal Mixed Models for individual claims reserving. The paper ends with the illustration of the presented techniques in section 4 and 5 on the data set simulated.