Integrated Model Of GLM And Neural Network And Its Application

Generalized linear model is the standard model of non life insurance actuarial,which is widely used in non life insurance rate determination and reserve evaluation.In the prediction of claim frequency,Poisson regression model and negative binomial regression model are commonly used.Although the generalized linear model has a good explanatory power,it can not well reflect the complex relationship between the data.The neural network model has a good model effect,which can well reveal the complex relationship between the data.The main goal of this paper is to combine GLM(generalized linear model)with neural network model to obtain better prediction effect and make the model have explanatory power at the same time.This paper first introduces multiple claim frequency models and establishes Lasso-Gamlss(generalized additional models for location,scale and shape)model for the problem of model variable selection.Then it introduces multiple deep learning neural networks into non life insurance actuarial.The analysis results based on actual vehicle insurance data show that the effect of neural network model is better than that of traditional claim frequency model.Based on the above results,combined with the generalized linear model and neural network model,CANN(combined actual neural network)model is introduced.Because GAM(generalized additive models)has better fitting effect than generalized linear model,it is extended to CANN of generalized additive model.Because CNN(revolution neural network)model can automatically select variables,it has good model effect in the case of many variables,so it is extended to CANN of CNN model.In order to improve the explanatory power of CANN model,this paper proposes an integrated model based on deep learning neural network to modify GLM residuals.Firstly,it studies from the perspective of theory,explains the advantages of the relevant integration model,and then establishes the integration model.Firstly,the generalized linear model is used to predict the loss data,and the residual between the predicted value and the observed value is calculated.Several neural network models are used to predict the loss data,and several models with relatively good results and the optimal parameters of the model are selected.Taking loss influencing factors as independent variables and residuals as dependent variables,the improved BP(back propagation),DNN(deep neural network)and CNN models are established to fit the residuals,and then the prediction value of the generalized linear model is modified by the residual prediction value of the deep neural network to obtain the prediction result.Based on the idea of integration,two kinds of integration models are established by selecting the appropriate model from the residual correction model.The first method is to integrate the residual correction model with DNN model,and the second method is to integrate the prediction model with linear regression model.Through the empirical study,it is found that the residual correction model is better than the generalized linear model,and the result is similar to that of the neural network model.The effect of the integrated model is better than that of the single residual correction model,and the effect of the second integrated method is better than that of the first integrated method.The results show that the integrated model can improve the prediction effect of vehicle insurance claim frequency while retaining the explanatory power of traditional GLM model.