A Generalized Linear Model With Smoothing Effects For Claims Reserving

Since21century, Chinese insurance industry has developed drastically. It supplies the insurance companies with not only positive developing opportunities due to the prosperous financial market and an open economic environment, but also hard challenges to insurers. With ongoing completing in the national insurance system, insurance companies and insurance supervising institutions gradually focus on the problem about depositing of claims reserving.As the development of computer technology and statistics methods, in the passing20years, establishing the model to predict the claims reserving became very hot in actuarial research. Nowadays insurance companies mostly use deterministic chain-ladder methods to estimate claims reserving. The deterministic method is very simple and direct in theory but it just produces the estimation on a point. Moreover it’s very difficult to examine the results in current statistical criterions. Therefore it can’t fulfill the requirement of analyzing dynamical financial data in insurance companies. So doing research basing on a stochastic model is better than the original deterministic method. For the sake of not only utilizing the information in the data, but also improving the precision of estimation on claims reserving, many statistical theory and methods are being used in researching how to predict the claims reserving, including generalized linear model that naturally over-extend in linear model and is extremely fitting to actuarial research due to its own superiority in theory. Therefore it’s widely used in researching claims revering as one of stochastic models.Many scholars have done a lot of research on development factors of claims reserving basing on a generalized linear model. Here we study further on the basis of achievement of England and Verrall who proposed a method related with a generalized linear model analyzing the development factors. In this paper we focus on how to realize their idea with the help of R procedure to reparameterize the whole model and make smoothing effect on original development factors as well as the calendar year parameter. We can still keep the structure of GLM model completely. In addition, we put up with a method using bootstrap to select the prefect smoothing model to predict interesting development factors. Ultimately we can also implement model selection into the procedure, and then distinguish those results. We make a conclusion that the different effects on the claims reserving estimation made by selection on different critical points or risk distributions are based on the individual data. Secondly difference results got by between AIC and BIC is not very distinct as opposed to the conclusion of original paper.