# LUP Student Papers

## LUND UNIVERSITY LIBRARIES

### Spatial Statistical Modeling of Insurance Risk

(2017) FMS820 20162
Mathematical Statistics
Abstract
The aim of this thesis is to provide a statistical method for assessing the relative insurance risk associated with the policyholders geographical location. Number of claims and claims cost are modeled separately, where the Poisson distribution is assumed for the former and the Gamma distribution is assumed for the latter. The models are based on a Bayesian approach, and inference is made using Integrated Nested Laplace Approximation (INLA). It is shown that an ordinary generalized linear model is sufficient for the Gamma distributed claims cost - while the model for number of claims can be improved by combining the ordinary generalized linear model with a spatial component in a conditional auto regressive model. In this study car... (More)
The aim of this thesis is to provide a statistical method for assessing the relative insurance risk associated with the policyholders geographical location. Number of claims and claims cost are modeled separately, where the Poisson distribution is assumed for the former and the Gamma distribution is assumed for the latter. The models are based on a Bayesian approach, and inference is made using Integrated Nested Laplace Approximation (INLA). It is shown that an ordinary generalized linear model is sufficient for the Gamma distributed claims cost - while the model for number of claims can be improved by combining the ordinary generalized linear model with a spatial component in a conditional auto regressive model. In this study car insurance data from If P\&C Insurance was used together with spatial referenced data of high resolution, provided by Insightone. (Less)
Popular Abstract
An epidemiologist approach to improved car insurance premiums

When deciding the premium for a specific car insurance, insurers take a plethora of factors, such as age and area of residence, into consideration. But a new approach is bringing added resolution to the picture.

To price their insurance contracts in an optimal way, the insurance company needs to do their utmost in accurately predicting the future cost of claims from the insured policyholder. For this purpose they use different explanatory variables. At If, the geo-location of the policyholder has been one of these variables for a long time. As an example one can imagine that a car gets more frequently damaged in a city, than in a more sparsely populated area, due to the... (More)
An epidemiologist approach to improved car insurance premiums

When deciding the premium for a specific car insurance, insurers take a plethora of factors, such as age and area of residence, into consideration. But a new approach is bringing added resolution to the picture.

To price their insurance contracts in an optimal way, the insurance company needs to do their utmost in accurately predicting the future cost of claims from the insured policyholder. For this purpose they use different explanatory variables. At If, the geo-location of the policyholder has been one of these variables for a long time. As an example one can imagine that a car gets more frequently damaged in a city, than in a more sparsely populated area, due to the denser traffic. But it is possible to detect differences in risk even on a geographically very detailed level.

As the areas become smaller, the amount of observed claim data in each area gets scarcer. Previously at If, the geographic assessment of risk was based on demographic and socio-economic variables from each location to bypass the issue of data scarcity. Using a new approach to the assumed model, If looks to improve insurance pricing by allowing neighbouring areas to borrow information from each other.

The model tested in a case study utilizes a geographical division provided by the analysis company Insightone. The areas are of varying size and densely populated areas can sometimes be as small as only an apartment block. The method relies upon a model that was developed for image restoration, and has been applied in epidemiology for estimating the risk of a disease given the number of occurrences at each location.

By using the variables from each location and at the same time allowing the risk in an area to be dependent on its neighbours, the prediction can be improved if a spatial pattern is recognized.

In the case study on vehicle hull damage insurance from If, it is shown that the new approach works well for predicting the number of claims, but that information from neighbours do not improve predictions of average claim cost. The result also demonstrates that the insurance company can improve their pricing by accounting for neighbourhood structure, when estimating number of accidents.

This way of assessing risk associated with geographical location could very well be applied to other insurance products, and the method could prove efficient in cases where good demographic or socio-economic variables do not exist. So, if you know what happened around a policy - why don't you peek around the corner to improve prediction? (Less)
author
supervisor
organization
alternative title
An epidemiologist approach to improved car insurance premiums
course
FMS820 20162
year
type
H2 - Master's Degree (Two Years)
subject
keywords
Insurance, Spatial modeling, Geographical pricing, Bayesian hierarchical modeling, Integrated Nested Laplace Approximation
report number
LUTFMS-3313-0017
ISSN
1404-6342
language
English
id
8902318
2017-02-07 08:19:58
date last changed
2017-02-07 08:19:58
```@misc{8902318,
abstract     = {The aim of this thesis is to provide a statistical method for assessing the relative insurance risk associated with the policyholders geographical location. Number of claims and claims cost are modeled separately, where the Poisson distribution is assumed for the former and the Gamma distribution is assumed for the latter. The models are based on a Bayesian approach, and inference is made using Integrated Nested Laplace Approximation (INLA). It is shown that an ordinary generalized linear model is sufficient for the Gamma distributed claims cost - while the model for number of claims can be improved by combining the ordinary generalized linear model with a spatial component in a conditional auto regressive model. In this study car insurance data from If P\&C Insurance was used together with spatial referenced data of high resolution, provided by Insightone.},
author       = {Tufvesson, Oskar},
issn         = {1404-6342},
keyword      = {Insurance,Spatial modeling,Geographical pricing,Bayesian hierarchical modeling,Integrated Nested Laplace Approximation},
language     = {eng},
note         = {Student Paper},
title        = {Spatial Statistical Modeling of Insurance Risk},
year         = {2017},
}

```