Spatial Statistical Modelling of Insurance Claim Frequency
(2022) In Master's Theses in Mathematical Sciences FMSM01 20212Mathematical Statistics
- Abstract
- In this thesis a fully Bayesian hierarchical model that estimates the number of aggregated insurance claims per year for non-life insurances is constructed using Markov chain Monte Carlo based inference with Riemannian Langevin diffusion. Some versions of the model incorporate a spatial effect, viewed as the relative spatial insurance risk that originates from a policyholder's geographical location and where the relative spatial insurance risk is modelled as a continuous spatial field. It is shown that the inclusion of a spatial effect derived from a Gaussian Markov random field with Matérn covariance in a generalised linear mixed model (GLMM) has better predictive performance regarding the number of aggregated claims in an insurance... (More)
- In this thesis a fully Bayesian hierarchical model that estimates the number of aggregated insurance claims per year for non-life insurances is constructed using Markov chain Monte Carlo based inference with Riemannian Langevin diffusion. Some versions of the model incorporate a spatial effect, viewed as the relative spatial insurance risk that originates from a policyholder's geographical location and where the relative spatial insurance risk is modelled as a continuous spatial field. It is shown that the inclusion of a spatial effect derived from a Gaussian Markov random field with Matérn covariance in a generalised linear mixed model (GLMM) has better predictive performance regarding the number of aggregated claims in an insurance portfolio compared to GLMMs that lack such a spatial effect. (Less)
- Popular Abstract
- The geographic rating factor used to determine the insurance risk originating from the geographical location of a policyholder can be modelled with a continuous spatial dependence. Continuous models allow the geographic risks to vary in larger pricing areas which is not the case with constant, or discrete models. Constant geographic risks can cause the geographic risks of larger pricing areas to have a greater influence on neighbouring pricing areas than feasible.
The purpose of insurances is to protect against financial loss. To be insured by an insurance, the policyholder has to pay a premium. The price of the premium needs to be proportionate to the size of the future and uncertain losses of the policyholder. These losses may or may... (More) - The geographic rating factor used to determine the insurance risk originating from the geographical location of a policyholder can be modelled with a continuous spatial dependence. Continuous models allow the geographic risks to vary in larger pricing areas which is not the case with constant, or discrete models. Constant geographic risks can cause the geographic risks of larger pricing areas to have a greater influence on neighbouring pricing areas than feasible.
The purpose of insurances is to protect against financial loss. To be insured by an insurance, the policyholder has to pay a premium. The price of the premium needs to be proportionate to the size of the future and uncertain losses of the policyholder. These losses may or may not be financial, but they need to be reducible to financial terms. To determine the future and uncertain losses for a specific policyholder, an insurance company looks at the individual traits of the policyholder and compares these traits with the traits of policyholders that have incurred historical losses. The insurance company then assumes that these traits are indicative for future losses. How indicative certain traits are, can be quantified and used to estimate future losses with probabilities. These probabilities are needed to define the risk premium which is based on the number of times during a specific period a policyholder is expected to suffer a loss together with the expected sizes of these losses. With the risk premium it is possible to determine a proportionate price for an insurance policy. One of the traits an insurance company can look at is called the geographic factor, or spatial effect. The spatial effect indicates how much of a policyholder's insurance risk originates from the region which the policyholder resides in. It was shown in a case study performed by Tufvesson, O. (2016) that the spatial effect derived from a discrete model improved claim frequency predictions, i.e. how many insurance claims will be made during a specific period. However, for the cost, or severity of the claims no spatially associated risk was found.
Based on real data it has been shown in a case study performed by Faller, D. in 2021 that a continuous spatial model also improves claim frequency predictions.
The continuous model has less requirements regarding the resolution of the geographic data used to determine the geographic rating factors compared to discrete models. Discrete models require micro-geographical data, e.g. instead of estimating the spatial effect for a part of Stockholm's inner city with 13,831 areas, as done in Tufvesson's discrete model, the continuous model estimates the spatial effect for the whole of Brazil with 3,109 areas. The relaxed requirements regarding the geographic data in the continuous model enable accurately priced insurances with the use of a spatial effect, even if micro-geographical data is not available. (Less)
Please use this url to cite or link to this publication:
http://lup.lub.lu.se/student-papers/record/9073261
- author
- Faller, Daniel LU
- supervisor
- organization
- course
- FMSM01 20212
- year
- 2022
- type
- H2 - Master's Degree (Two Years)
- subject
- keywords
- Insurance risk, claim frequency, Markov chain Monte Carlo (MCMC), Riemann manifold Metropolis adjusted Langevin algorithm (MMALA), spatial statistics, Gaussian Markov random field (GMRF), preconditioned Crank Nicolson Langevin algorithm (pCNL), Gibbs sampling, Bayesian hierarchical modelling, high dimensional, shrinkage prior, horseshoe prior, regularisation.
- publication/series
- Master's Theses in Mathematical Sciences
- report number
- LUTFMS-3437-2022
- ISSN
- 1404-6342
- other publication id
- 2021:E7
- language
- English
- id
- 9073261
- date added to LUP
- 2022-01-26 09:34:38
- date last changed
- 2022-02-10 14:56:44
@misc{9073261,
abstract = {{In this thesis a fully Bayesian hierarchical model that estimates the number of aggregated insurance claims per year for non-life insurances is constructed using Markov chain Monte Carlo based inference with Riemannian Langevin diffusion. Some versions of the model incorporate a spatial effect, viewed as the relative spatial insurance risk that originates from a policyholder's geographical location and where the relative spatial insurance risk is modelled as a continuous spatial field. It is shown that the inclusion of a spatial effect derived from a Gaussian Markov random field with Matérn covariance in a generalised linear mixed model (GLMM) has better predictive performance regarding the number of aggregated claims in an insurance portfolio compared to GLMMs that lack such a spatial effect.}},
author = {{Faller, Daniel}},
issn = {{1404-6342}},
language = {{eng}},
note = {{Student Paper}},
series = {{Master's Theses in Mathematical Sciences}},
title = {{Spatial Statistical Modelling of Insurance Claim Frequency}},
year = {{2022}},
}