Mixture Modelling for Auto Insurance

X. Sheldon Lin
Professor
Department of Statistical Sciences
University of Toronto

Wednesday, 17 April 2024
10:30 AM – 12:00 PM
Venue: Gaia Lecture Theatre 5 (#ABS-02-LT5)
Chairperson: Associate Prof Wenjun Zhu 

Abstract

Property and casualty (P&C) insurance is always policy specific. Since policyholders possess different risk characteristics, a P&C insurance portfolio is highly heterogeneous. As a result, modelling and analyzing the claims (frequency and severity), risk classification, ratemaking and reserve determination entail many challenges, especially from a data-driven modelling perspective. 

In this presentation, we present a mixture modelling framework to address these challenges. In particular, we propose the use of mixture of experts models that are very flexible, are capable of incorporating policy attributes in a nonlinear manner and can leverage policyholders’ claim history through random effects. Furthermore, the mixture structure of the models allows to classify policyholders into groups with similar risk profiles.  Parameter estimation can be performed through EM algorithms. In the case that random effects are included, the estimation can be obtained by a stochastic variational algorithm, which is numerically efficient and scalable to large insurance portfolios. Real data applications show that the  proposed framework outperforms the classical benchmark models commonly used in practice  (Logistic and Lognormal GL(M)M) in terms of goodness-of-fit to data, while offering intuitive and interpretable characterization of policyholders’ risk profiles to adequately reflect their claim history.

About the Speaker

X. Sheldon Lin, ASA, ACIA, is a Professor of Actuarial Science at the University of Toronto and serves as an Editor for Insurance: Mathematics and Economics. His recent research is on data-driven nonlinear regression modelling for insurance rate-making and risk management of large insurance portfolios. The research aims to develop new and implementable methodology and technologies for insurance.