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A CLASS OF MIXTURE OF EXPERTS MODELS FOR GENERAL INSURANCE: APPLICATION TO CORRELATED CLAIM FREQUENCIES

Published online by Cambridge University Press:  04 September 2019

Tsz Chai Fung ,
Andrei L. Badescu  and
X. Sheldon Lin
Tsz Chai Fung
Affiliation:
Department of Statistical Sciences University of Toronto100 St George Street Toronto, ON M5S 3G3, Canada E-Mail: tszchai.fung@mail.utoronto.ca
Andrei L. Badescu
Affiliation:
Department of Statistical Sciences University of Toronto100 St George Street Toronto, ON M5S 3G3, Canada E-Mail: badescu@utstat.toronto.edu
X. Sheldon Lin
Affiliation:
Department of Statistical Sciences University of Toronto100 St George Street Toronto, ON M5S 3G3, Canada E-Mail: sheldon@utstat.toronto.edu
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Abstract

This paper focuses on the estimation and application aspects of the Erlang count logit-weighted reduced mixture of experts model (EC-LRMoE), which is a fully flexible multivariate insurance claim frequency regression model. We first prove the identifiability property of the proposed model to ensure that it is a suitable candidate for statistical inference. An expectation conditional maximization (ECM) algorithm is developed for efficient model calibrations. Three simulation studies are performed to examine the effectiveness of the proposed ECM algorithm and the versatility of the proposed model. The applicability of the EC-LRMoE is shown through fitting an European automobile insurance data set. Since the data set contains several complex features, we find it necessary to adopt such a flexible model. Apart from showing excellent fitting results, we are able to interpret the fitted model in an insurance perspective and to visualize the relationship between policyholders’ information and their risk level. Finally, we demonstrate how the fitted model may be useful for insurance ratemaking.

Keywords

Erlang count modelsexpectation conditional maximization algorithmlogit-weighted gating functionsmixture of experts modelsmultivariate count regression
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 49 , Issue 3 , September 2019 , pp. 647 - 688
Copyright
© Astin Bulletin 2019 

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