The Role of Data Mining Techniques and External Data in Enhancing Generalized Linear Models in Insurance: Practice Questions and Solutions

This section of the study guide is intended to provide practice problems and solutions to accompany the pages of Basic Ratemaking, cited below. Students are encouraged to read these pages before attempting the problems. This study guide is entirely an independent effort by Mr. Stolyarov and is not affiliated with any organization(s) to whose textbooks it refers, nor does it represent such organization(s).

Some of the questions here ask for short written answers based on the reading. This is meant to give the student practice in answering questions of the format that will appear on Exam 5. Students are encouraged to type their own answers first and then to compare these answers with the solutions given here. Please note that the solutions provided here are not necessarily the only possible ones.

Source:
Werner, Geoff and Claudine Modlin. Basic Ratemaking. Casualty Actuarial Society. 2009. Chapter 10, pp. 181-183.

Original Problems and Solutions from The Actuary's Free Study Guide

Problem S5-83-1.

(a) What is the purpose of cluster analysis?

(b) With what kinds of rating variables is cluster analysis most frequently used?

Solution S5-83-1. This problem is based on the discussion of cluster analysis by Werner and Modlin, p.181.

(a) The purpose of cluster analysis is "to combine small groups of similar risks into larger homogeneous categories or 'clusters.'" This enables the variables based on the resulting clusters to be more easily incorporated into generalized linear models (GLMs), since there are fewer variables and more data that would be relevant to each variable.

(b) Cluster analysis is most frequently used with rating variables pertaining to geography, where small geographic areas, such as zip codes, with similar experience might be grouped into a single cluster.

Problem S5-83-2.

(a) What does the acronym CART stand for?

(b) How does CART work? (Briefly describe just the basics.)

(c) Name one purpose that CART can help actuaries accomplish.

Solution S5-83-2. This problem is based on the discussion of CART by Werner and Modlin, p.181.

(a) The acronym CART stands for Classification and Regression Trees.

(b) CART employs classification trees based on if-then logical conditions. For instance, variable X can be the initial variable being examined. If variable X has value a, then variable Y is examined; if variable X has value b, then variable Z is examined, which may or not be the same variable as Y. The "tree" is formed with each option within a variable leading to a separate "branch" of the tree. The order in which variables are examined may depend on the "branches" of the tree that are being followed.

(c) According to Werner and Modlin, p.181, CART can help 1) "identify the strongest list of initial variables", 2) "determine how to categorize each variable", and 3) "detect interactions between variables." Any of the above items suffices as an answer. Other valid answers may also be possible.

Problem S5-83-3.

(a) What does the acronym MARS stand for?

(b) How does MARS work? (Briefly describe just the basics.)

(c) Name one purpose that MARS can help actuaries accomplish.

Solution S5-83-3. This problem is based on the discussion of MARS by Werner and Modlin, p.181.

(a) The acronym MARS stands for the Multivariate Adaptive Regression Spline.

(b) MARS is an algorithm that "operates as a multiple piecewise linear regression where each breakpoint defines a region for a particular linear regression equation" (Werner and Modlin, p.181).

(c) According to Werner and Modlin, p.181, MARS can help 1) "select breakpoints for categorizing continuous variables" and 2) "detect interactions between variables." Any of the above items suffices as an answer. Other valid answers may also be possible.

Problem S5-83-4.

(a) Briefly describe the basics of what neural networks do.

(b) What element of good models have neural networks often been criticized as lacking?

(c) Name one purpose that a neural network can help actuaries accomplish.

Solution S5-83-4. This problem is based on the discussion of neural networks by Werner and Modlin, p.182.

(a) Neural networks employ training algorithms that are applied to test data and that are able to "learn" the data's structure.

(b) Neural networks have been criticized as lacking transparency. Neural networks use extremely sophisticated and complex algorithms, which are not always easily communicable to all parties who need to know about how the model works.

(c) A neural network's results can be fed into a GLM and can identify areas within the GLM that might need improvement - such as taking account of a missing interaction (Werner and Modlin, p.182).

Problem S5-83-5. Name three kinds of external data that insurers have increasingly come to use after GLMs have been adopted.

Solution S5-83-5. The following external data types are discussed by Werner and Modlin, p. 182:

1. "Geo-demographics (e.g., population density of an area, average length of homeownership in an area)";

2. "Weather (e.g., average rainfall or number of days below freezing of a given area)";

3. "Property characteristics (e.g., square footage of a home or business, quality of the responding fire department";

4. "Information about insured individuals or businesses (e.g., credit information, occupation)."

Any three of the above suffice as an answer. Other valid answers may also be possible.

See other sections of The Actuary's Free Study Guide for Exam 5.