Spatial analysis ranges from simple univariate descriptive statistics to complex multivariate analyses and is typically used to investigate spatial patterns or to identify spatially linked consumer behaviours in insurance. This paper investigates if the incorporation of publicly available spatially linked demographic census data at population level is useful in modelling customers’ lapse behaviour (i.e. stopping payment of premiums) in life insurance policies, based on data provided by an insurance company in Ireland. From the insurance company’s perspective, identifying and assessing such lapsing risks in advance permit engagement to prevent such incidents, saving money by re-evaluating customer acquisition channels and improving capital reserve calculation and preparation. Incorporating spatial analysis in lapse modelling is expected to improve lapse prediction. Therefore, a hybrid approach to lapse prediction is proposed – spatial clustering using census data is used to reveal the underlying spatial structure of customers of the Irish life insurer, in conjunction with traditional statistical models for lapse prediction based on the company data. The primary contribution of this work is to consider the spatial characteristics of customers for life insurance lapse behaviour, via the integration of reliable government provided census demographics, which has not been considered previously in actuarial literature. Company decision-makers can use the insights gleaned from this analysis to identify customer subsets to target with personalized promotions to reduce lapse rates, and to reduce overall company risk.

While generalized linear models have become the insurance industry's standard approach for claim modelling, the approach of utilizing a single best model on which predictions are based ignores model selection uncertainty. An additional feature of insurance claim data sets is the common presence of categorical variables, within which the number of levels is high, and not all levels may be statistically significant. In such cases, some subsets of the levels may be merged to give a smaller overall number of levels for improved model parsimony and interpretability. Hence, clustering of the levels poses an additional model uncertainty issue. A method is proposed for assessing the optimal manner of collapsing factors with many levels into factors with smaller numbers of levels, and Bayesian model averaging is used to blend model predictions from all reasonable models to account for selection uncertainty. This method will be computationally intensive when the number of factors being collapsed or the number of levels within factors increases. Hence, a stochastic approach is used to quickly identify the best collapsing cases across the model space.1. Should a categorical predictor be included? 2. When included, should certain levels be merged together? 3. When included and with certain levels merged, how much confidence should be placed on this clustering of levels and this model?Therefore, factor collapsing (FC) and BMA are considered to improve model predictions, with a focus on clustering categorical levels within factors so that the number of levels can be reduced, and thus, model parsimony and interpretability improved. The structure of this article is as follows: in Section 2 data sets used are introduced; Section 3 briefly reviews BMA, introduces the method of FC incorporated within BMA (FC-BMA) and discusses how to select the optimal clustering of categories in a computationally efficient way; Section 4 tests and compares the different

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The mvClaim package in R provides flexible modelling frameworks for multivariate insurance claim severity modelling. The current version of the package implements a parsimonious mixture of experts (MoE) model family with bivariate gamma distributions, as introduced in Hu et al., and a finite mixture of copula regressions within the MoE framework as in Hu & O’Hagan. This paper presents the modelling approach theory briefly and the usage of the models in the package in detail. This package is hosted on GitHub at https://github.com/senhu/.

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