Prediction of Claim Probability with Excess Zeros

Abstract

Non-life insurance pricing is based on two components: claim severity and claim frequency. These components are used to estimate expected pure premium for the next policy period. Generalized linear models (GLM) are widely preferred for the estimation of claim frequency and claim severity due to the ease of interpretation and implementation. Since GLMs have some restrictions such as exponential family distribution assumption, more flexible Machine Learning (ML) methods are applied to insurance data in recent years. ML methods use learning algorithms to establish relationship between the response and the predictor variables as an intersection of computer science and statistics. Because of some insurance policy modifications such as deductible and no claim discount system, excess zeros are usually observed in claim frequency data. In the presence of excess zeros, prediction of claim probability can be a good alternative to the prediction of claim numbers since positive numbers are rarely observed in the portfolio. Excess zeros create imbalance problem in the data. When the data is highly imbalanced, predictions will be biased toward majority class due to the priors and predicted probabilities may be uncalibrated. In this study, we are interested in claim occurrence probability in the presence of excess zeros. A Turkish motor insurance dataset that is highly imbalanced is used for the case study. Ensemble methods that are popular ML approaches are used for the probability prediction as an alternative to logistic regression. Calibration methods are applied to predicted probabilities and results are compared.