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Summary
This paper gives a brief description of the main analytic tools and approaches to modeling found in personal lines pricing literature and employed by the insurance business.
Rating methodology has evolved over the years into a well-defined science, and traditional statistical methods such as regression analysis continue to be the predominant modeling tool of choice. With the advent of new technologies such as GLM (Generalized Linear Model) Neural Network and Decision Trees, however, actuaries are endeavoring to improve upon existing models by augmenting their traditional tools with the latest technology. Even in companies where traditional regression still prevails for the purposes of rating, actuaries are using data mining technology to better establish and characterize relationships in their data for both underwriting and pricing decisions.
The aim of this article is the comparison of parametric and non-parametric statistical methods applied to the same database. In general, there are visible differences between a parametric and a non-parametric curve estimate. It is therefore quite important to compare these methods, in order to see which one is more appropriate and in which cases.
In fact, the use of all these techniques makes it possible to investigate phenomena characterized by a complex informative patrimony. The reason why these statistical methods are widely used lies in their power of synthesis, their ability to carry out complete analysis and their clarity. In fact, the purpose of these techniques is to investigate whether data under review can be represented by some relation among parameters and find the simplest possible solution which, however, does not lose the power to predict future trends of the phenomena under study.
The database used for this comparison is a Third Party Liability motor insurance portfolio, and the scope of the analysis is the definition of a technical tariff, using all the rating parameters about the policyholder and the owned car. The nature of the data and the problems faced, normally determine the choice of the analytical technique. In our case, the database contains information of different nature and importance, which must be appropriately considered and summarised.
The multivariate analysis (parametric or non-parametric, it does not matter) identifies the dependency and interactions among these variables, even when their relationship is not obvious. It makes then possible to present a synthesis of explanatory values, which minimize the variability of real data and isolate the effect of each variable with respect to all the others.
The results obtained with the parametric methods (Generalized Linear Model - GLM), and those obtained with the non-parametric ones (CART, CHAID, Neural Networks) will be compared in terms of:
- practical applications and facility of usage;
- goodness of fit among the estimates, when possible.
The comparison in terms of how easy each method is for the application in the insurance field is relatively simple. Much more difficult is the comparison in terms of test statistics. In fact, it is surprising that, although the non-parametric approach in modeling regression relationships has received a lot of attention recently, there are only a few theoretical results on how to compare parametric with
non-parametric fits. In some cases, we need the use of Bootstrap techniques to do it.
What can a GLM modeller learn from Neural Network and Decision Tree procedures and how can a Neural Network be used to extend a GLM model? These are the questions discussed on this paper. |
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She is a consultant actuary with Tillinghast – Towers Perrin in the areas of Reserves Analysis, Data Mining and Rating Make. Cristina Mano has a degree in Actuarial Science and Mathematics from the Federal University of Rio de Janeiro (UFRJ) and Statistics from ENCE/IBGE.
She holds a Master Degree in Statistics from Federal University of Rio de Janeiro (UFRJ). She published her thesis on Insurance Rating Make and the Theory of Credibility, which gave her the Ph.D. from the Production Engineering Department of the Federal University of Rio de Janeiro (UFRJ).
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