Simple Compound Risk Model with Dependant Structure

Abstract

There have been fewer trials to address the claim severity in the development of optimal bonus-malus system (BMS), while the claim frequency has been dealt with a lot. In this article, the generalized linear mixed model (GLMM) was incorporated to address the severity, frequency, and their dependency simultaneously with 5 years insurance panel data. Also, estimated individual random effect coefficient from training set and past claim was utilized as a predictor of future loss. From the result of analysis, it was revealed that GLMM had the better fit than its alternatives including simple generalized linear model, dependency between the frequency and severity was significant, and estimated random effect coefficient predicted the future loss better as the length of training set increased. These results provide the rationale to reflect both the past frequency and past severity to construct the optimal BMS, and considering dependence between frequency and severity in the derivation of motor insurance premium.