The talk starts at 12:15.

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Speaker: Jens Christian Wahl, NR

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Title: Spatial Modelling of risk premiums for water damage insurance

Abstract: In this paper we compare different spatial models for modelling the risk

premium for water damage insurance on the level of the policyholder. We

evaluate four models that take the spatial variability into account: (1) the

Intrinsic Markov Random Field (ICAR) model; (2) the Besag, York, Mollier

(BYM) model; (3) the independent random effects model; and (4) a spatial

spline model. The models are compared on a huge dataset from the Norwegian

insurance company Gjensidige containing seven million observations

of policyholders during the period 2011-2018. While Bayesian methods are

most frequently used for inference in Gaussian Markov Random Field models,

we take a frequentist approach and estimate the model parameters using the

method proposed in Wood et al. (2014, 2017); Li and Wood (2020). Using

the R package mgcv, we compare the different models for claim frequency,

claim size and combined in a risk premium model in a comprehensive cross-validation

study. Practical measures such as the loss ratio lift, double lift and

Gini index are used to compare performance. Finally, we also compare mgcv

with INLA (Rue et al., 2009) and show that for reasonable big datasets we

get identical estimates at a much lower computational cost.

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