Abstract
This paper explores the application of spatial models to non-life insurance data focused on the multi-risk home insurance branch. In the pricing modelling and rating process, spatial information should be considered by actuaries and insurance managers because frequencies and claim sizes may vary by region and the premium should be different considering this rating variable. In addition, it is relevant to examine the spatial dependence due to the fact that the frequency of claims in neighbouring regions is often expected to be more closely related than those in regions far from each other. In this paper, a comparison between spatial models, such as spatial autoregressive models (SAR), the spatial error model (SEM), and the spatial Durbin model (SDM), and a non-spatial model has been developed. The data used for this analysis are for a home insurance portfolio located in Spain, from which we have selected peril of water coverage.
Highlights
According to Investigación Cooperativa de Entidades Aseguradoras-Spanish Association for Cooperative Research between Insurance Entities and Pension Funds (ICEA), in 2020, approximately 39% of home insurance claims in Spain were due to water damage, 12.9% of which were associated with atmospheric phenomena
Spatial econometric models have been defined to model the variable severity of losses associated with insurance policy claims
In the case of the spatial modelling of claim severity, the spatial autoregressive model (SAR), the spatial error model (SEM), and the spatial Durbin model (SDM) have been considered in order to develop a comparison between spatial models and non-spatial model as a baseline
Summary
Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. In the Bayesian context, spatial modelling applied to actuarial science has been developed by Gschlößl and Czado [8,9], where the inclusion of spatial effects is considered to model claim frequency and claim size, showing more accurate predictions (car insurance) Within this framework, it is significant to mention the application of the Besag, York, and Mollie (BYM) model to analyse the claim frequency and claim size, taking spatial dependence into account in the pricing process [10]. As has been reflected in the actuarial field for certain risks such as crop insurance or car insurance, spatial econometric models have been applied, especially in the Bayesian context [8,9,10] This clearly demonstrates actuaries’ interest in spatial econometrics and the importance of including it as a relevant framework within actuarial science.
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