In The Second Stage GLMM Prediction Outstanding Claims Reserve Application

As operational risks commercial companies, the insurance company attachesgreat importance to the problem of estimating the outstanding Claims Reserve. If weget a overestimated in corporate earnings, it can be resulting in the illusion ofsolvency of the company. On the contrary, if the outstanding claim reserves isestimated too little, it will not only lead to take on more tax revenue because of theincreased profit,but also lead to serious consequences of bankruptcy when theoutstanding Claims Reserve can’t pay the occurrence of claims. The phenomenon isnot uncommon in the beginning of this century. Exploration of the estimation methodof the outstanding Claims Reserve becomes the direction of many scholars and theyhave proposed many estimation methods, such as deterministic models, stochasticmodels and dynamic models. The generalized linear models and generalized linearmixed models of the stochastic model are the very popular tools in the actuarialestimate. However, can it be useful to add random-effects in the generalized linearmodel to built generalized linear mixed model to estimate the outstanding ClaimsReserve. Few literature make them comparing with each other.First of all, this paper introduces the basic concepts and calculation methods ofseveral deterministic models used by insurance companies in China in the provisionfor outstanding claims reserve. The paper also points out the defects of thedeterministic models and the necessity of recommending the stochastic models. Thestochastic models introduced in the paper are the generalized linear model andgeneralized linear mixed models. We give a brief introduction of their modelstructures, parameter estimation methods and the evaluation of models.Secondly, the article describes the two-stage generalized linear mixed models,and elaborates its principle and its estimation in detail, and point out its advantage inestimating the outstanding Claims Reserve. Thirdly, the structures of the stochastic model that are given in the paper used toestimate the outstanding Claims Reserve. The meaning of the parameters and themethods and the steps are made a brief introduction in the paper.Finally, the article makes an empirical analysis using generalized linear models,two-stage generalized linear models, generalized linear mixed models and two-stagegeneralized linear mixed model to estimate the outstanding Claims Reserve, andcompares their estimation accuracy through calculating their average deviation andthe mean square bias.Through comparing the results with each stochastic model used to estimate theoutstanding Claims Reserve, the paper is not only verifying that the generalized linearmixed model is more suitable than the generalized linear model to estimate theoutstanding Claims Reserve, but also verifying that the accuracy estimated bytwo-stage generalized linear mixed models is indeed better than the other models,proving the feasibility of two-stage generalized linear mixed models in the estimationof the outstanding Claims Reserve. We also found that using this method to estimatethe amount of outstanding claims reserve can get a moderate result compared withother stochastic models. The result is in the middle position, neither too littleestimated to result in potential loss risk, not overly conservative estimate, resulting ina reduction of book profit of the company. The article also find that it is more betterwhen we make the starting years factors as random effect and the development yearsfactors as fixed effect than make the starting years factors as fixed effect and thedevelopment years factors as random effect.In the last part of the article, the author makes a summary of the full paper, andindicates the deficiencies of this research, and some items for future research areproposed.