Zero-inflated claim number models

Specialeforsvar ved Carina Schmidt

Titel: Zero-inflated claim number models

Abstract: Frequently used models for the number of claims in insurance are the Poisson and the Negative Binomial regression models. Sometimes, the claim number data are zero-inflated, meaning that the number of observed zeros exceeds the number of expected zeros under the distributional assumptions. This thesis presents the zero-inflated Poisson regression model and the zero-inflated Negative Binomial regression model to accommodate the excess zeros for insurance claim number data. We consider historical claim data with explanatory variables describing the policy, which is carrying a deductible. Estimation is accomplished by applying the EM algorithm. We extend our models to include penalized regression splines, which allow non-linear dependencies between the number of claims and the explanatory variables. The estimation methods are tested on simulated data. Finally, we fit the models to a car insurance data set. Our results show that the estimation by the EM algorithm works well and the zero-inflated regression models predict the claim numbers of the data set very well

Vejleder:  Jostein Paulsen
Censor:    Mette Havning