Shengwang Meng, Zhengxiao Li

【Abstract】

Generalized linear models are widely used to predict the severity ofnon-life insurance. In generalized linear models, severity is often assumed to follow Gamma or inverse-Gaussian distribution, and covariates have linear effects on the linear predictor, which may affect the accuracy of predictions. This paper extendsthe present models in following aspects: shewed T distribution is used to take place of Gamma and inverse-Gaussian distribution; penalized splines are introduced tothe model to reflect the non-linear effect of continuous covariates; severity heterogeneity between distinct areas and severity dependence ofadjacentareas are considered in the model. An empirical study based on a set of motor insurance loss datashows that skewed T regression models with spatial effect may significantly improve the goodness of fit.

【Keywords】

skewed T distribution, spatial effect, severity