Dealing with continuous variables and geographical information in non life insurance ratemaking. Maxime Clijsters

Transcription

1 Dealing with continuous variables and geographical information in non life insurance ratemaking Maxime Clijsters

2 Introduction Policyholder s Vehicle type (4x4 Y/N) Kilowatt of the vehicle Age Age of the vehicle Age of the permit Postal code Professional use (Y/N) Categorical variable Continuous variable Multi-Level Factor Tariff?

3 Introduction GLMs remain a very important statistical regression technique for pricing car insurance products GAMs provide interesting insights in the underlying dependency structure, but come at a high computational cost GAM as a complementary modelling tool GLM = Generalized Linear Model GAM = Generalized Additive Model

4 AGENDA Binning continuous variables GAM to explore nonlinear effects GAM and regression trees for binning Modelling geographical information

5 Binning continuous variables GLM GLM is satisfying modelling tool Industry-wide standard Only categorical variables GAM Continuous variables High computational cost No parametric functional form

6 Binning continuous variables GAM to explore nonlinear effects

7 Binning continuous variables GAM to explore nonlinear effects

8 Binning continuous variables GAM to explore nonlinear effects Often not desirable to keep the continuous effect in the tariff» GAM has a high computational cost (iterative method)» GAM lacks a parametric functional form GAMs provide insight in defining risk homogeneous groupings of variables

9 Binning continuous variables GAM for binning Results of the GAM as a starting point for binning Broader categories where the risk is similar More categories when the risk varies a lot Defining boundaries by means of regression trees

10 Binning continuous variables Regression tree Divide variables into groups based on GAM estimate Find splits that minimize overall sum of squared errors Grow tree with desired number of classes Figure: The black coloured nodes correspond to the regression tree used, the blue coloured nodes are the following splits, and the light blue nodes are the subsequent splits

11 Binning continuous variables Binning results Figure: Visualization of the classes suggested by the regression tree

12 AGENDA Binning continuous variables Geographical information Modelling GLM without geographical information GAM with geographical information Visualizing and binning

13 Geographical information Introduction

14 Latitude Geographical information Introduction Bree: 51 07'08.8"N 5 38'32.5"E Longitude

15 Geographical information Step 1: GLM without geographical information

16 Geographical information Step 1: GLM without geographical information Predicted number of claims per district Observed number of claims per district

17 Geographical information Step 2: GAM with geographical information

18 Geographical information Step 2: GAM with geographical information

19 Geographical information Step 2: GAM with geographical information

20 Geographical information Visualizing and binning the geographic effect

21 Geographical information Visualizing and binning the geographic effect Problematic issue Different classification methods can yield dissimilar classes Maps are very sensitive to the classification method used Visualization of the same data can convey different impressions

22 Geographical information Visualizing and binning the geographic effect

23 Conclusion GLMs remain a very important statistical regression technique for pricing car insurance products. GAMs provide interesting insights in the underlying dependency structure, but come at a high computational cost. Care is needed when reading and interpreting choropleth maps Different classification techniques produce different results. Classification strongly affects the visual impressions readers obtain.

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