A general framework for modelling claim count data in general insurance based on the local mixed Poisson net

Abstract:

Over the last few decades, mixed Poisson (MP) regression models have been widely used for studying count regression type problems in many scientific fields such as sociology, econometrics, manufacturing, engineering, agriculture, biology, biometrics, genetics, medicine, sports, marketing and insurance. However, due to the ongoing emergence of a range of new technologies and data analytics tools, the highly data driven general insurance sector has become to pay increasing attention to deep learning models which often out-perform classical regression models which are too restrictive to learn complex features from data. On the other hand, mitigating interpretability issues is a crucial step for enabling actuaries to safely incorporate deep learning into their predictive modelling techniques. In this study, inspired by the work of Richman and Wuthrich (2021) and extending on our recent work by Tzougas and Li (2022), we introduce the local mixed Poisson net, which we call LocalMPnet, for modelling claim count data using an interpretable deep learning architecture. The proposed modelling framework provides sufficient flexibility for (i) modelling different levels of overdispersion, which is a direct consequence of unobserved heterogeneity due to systematic effects in the data, since as it is well known the tails of mixed Poisson distributions are similar to the tails of their mixing distributions, see Perline(1998) and (ii) taking advantage of the philosophy of representation learning while preserving the linear structure of MP regression models by using a skip connection which provides a linear modeling part around which the network model is built. For expository purposes we use choose the Negative Binomial (NB) deviance loss and we fit the LocalNBnet on a portfolio of motor insurance data. The results from indicate that the LocalNBnet provides better predictive performance than the NB regression and the plain-vanilla neural network.

Perline, R. (1998) Mixed Poisson distributions tail equivalent to their mixing distributions. Stat. Comput. 1998, 38, 229–233.
Richman, R., and Wuthrich, M. V. (2021). LocalGLMnet: interpretable deep learning for tabular data. Available at SSRN 3892015.
Tzougas, G., and Li, Z. (2022). Neural Network Embedding of the Mixed Poisson Regression Model for Claim Counts. (in submission)


Short Bio:

George Tzougas is an Associate Professor in the Department of Actuarial Mathematics and Statistics at Heriot Watt University in Edinburgh. He is also the Academic Director of the Scottish Financial Risk Academy and the Academic Chair of the IFoA’s Data Science Research working party Statistical Learning in Actuarial Applications. George previously held a tenured position in the Department of Statistics of the London School of Economics and Political Science, where he also served as Programme Director for the BSc in Actuarial Science and was the Liaison Officer with the IFoA. Previous to this George was a Lecturer in the Department of Statistics of University College Cork in Ireland. George's research interests lie on the interface between applied statistics, computational statistics, actuarial science and actuarial data science. His articles have appeared in world leading journals. In particular, his research primarily, but not exclusively, focuses on statistical learning applications, via estimation methods, such as the Expectation-Maximization (EM) algorithm, and computational aspects of deep learning in insurance and finance, including insurance ratemaking, setting appropriate levels of reserves and reinsurance, classification of green bonds and decarbonization. Finally, George's professional activities include a membership of the American Risk and Insurance Association,  a fellowship of the Royal Statistical Society and being a member of the reviewer board of MDPI's Risks journal.