Master's lecture in Statistics - Sunna Víðisdóttir

Master's student: Sunna Víðisdóttir

Title: Pricing of Automobile Insurance Policies using Generalized Linear Models and Lasso Regularization

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Faculty: Faculty of Physical Sciences

Advisor: Kristjana Ýr Jónsdóttir

Also member of the Masters committee: Gunnar Stefánsson, Professor at the Faculty of Physical Sciences

Examiner: Óli Páll Geirsson 

Abstract

The goal of this thesis is to create a predictive model for the expected claim cost of automobile insurance policies in Iceland. The proposed model is based on the characteristics of the policyholder and the insured vehicle, and reflects the risk associated with each policy. Most insurers base their premium structure on the expected cost of claims, making a model with good future prediction capabilities a valuable resource for the insurer.

The data used in this thesis is provided by the Icelandic insurance company TM, and contains policy and claims data from 2009-2017. Automobile insurance policies at TM are considered to consist of five product components, but since the components vary significantly in what they cover, each product component is modeled separately in this thesis. The predicted claim cost of each product component is determined by three parts; a frequency model of standard claims, a claim severity model of standard claims, and a large loss model. The main focus is on the frequency and severity models of standard claims which are modeled using a Poisson regression model and a gamma regression model respectively. This results in a compound Poisson distribution for the total cost of standard claims. The parameters of the two models are selected using lasso regularization. Finally, the predictive ability of the models is assessed using cross-validation.

The results show that the optimal predictive model for each of the five product components is quite different with regards to the choice of variables, demonstrating the importance of modelling each product component separately. The selected parameters for the frequency and the severity models of standard claims also differ, and by analyzing the two separately, a better understanding of the underlying risk is obtained. It is our believe that the modelling framework presented in this thesis can easily improve the current tariff structure at TM, and improve the competitiveness of the company.