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© Deloitte Consulting, 2004 Predictive Modeling for Property-Casualty Insurance James Guszcza, FCAS, MAAA Peter Wu, FCAS, MAAA SoCal Actuarial Club LAX September 22, 2004

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© Deloitte Consulting, 2004 2 Predictive Modeling: 3 Levels of Discussion Strategy Profitable growth Retain most profitable policyholders Methodology Model design (actuarial) Modeling process Technique GLM vs. decision trees vs. neural nets…

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© Deloitte Consulting, 2004 3 Methodology vs Technique How does data mining need actuarial science? Variable creation Model design Model evaluation How does actuarial science need data mining? Advances in computing, modeling techniques Ideas from other fields can be applied to insurance problems

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© Deloitte Consulting, 2004 4 Semantics: DM vs PM One connotation: Data Mining (DM) is about knowledge discovery in large industrial databases Data exploration techniques (some brute force) e.g. discover strength of credit variables Predictive Modeling (PM) applies statistical techniques (like regression) after knowledge discovery phase is completed. Quantify & synthesize relationships found during knowledge discovery e.g. build a credit model

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© Deloitte Consulting, 2004 Strategy: Why do Data Mining? Think Baseball!

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© Deloitte Consulting, 2004 6 Bay Area Baseball In 1999 Billy Beane (manager for the Oakland Athletics) found a novel use of data mining. Not a wealthy team Ranked 12 th (out of 14) in payroll How to compete with rich teams? Beane hired a statistics whiz to analyze statistics advocated by baseball guru Bill James Beane was able to hire excellent players undervalued by the market. A year after Beane took over, the As ranked 2 nd !

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© Deloitte Consulting, 2004 7 Implication Beane quantified how well a player would do. Not perfectly, just better than his peers Implication: Be on the lookout for fields where an expert is required to reach a decision based on judgmentally synthesizing quantifiable information across many dimensions. (sound like insurance underwriting?) Maybe a predictive model can beat the pro.

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© Deloitte Consulting, 2004 8 Example Who is worse?... And by how much? 20 y.o. driver with 1 minor violation who pays his bills on time and was written by your best agent Mature driver with a recent accident and has paid his bills late a few times Unlike the human, the algorithm knows how much weight to give each dimension… Classic PM strategy: build underwriting models to achieve profitable growth.

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© Deloitte Consulting, 2004 9 Keeping Score Billy Beane CEO who wants to run the next Progressive Beanes ScoutsUnderwriter Potential Team MemberPotential Insured Bill James stats Predictive variables – old or new (e.g. credit) Billy Beans number cruncher You! (or people on your team)

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© Deloitte Consulting, 2004 What is Predictive Modeling?

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© Deloitte Consulting, 2004 11 Three Concepts Scoring engines A predictive model by any other name… Lift curves How much worse than average are the policies with the worst scores? Out-of-sample tests How well will the model work in the real world? Unbiased estimate of predictive power

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© Deloitte Consulting, 2004 12 Classic Application: Scoring Engines Scoring engine: formula that classifies or separates policies (or risks, accounts, agents…) into profitable vs. unprofitable Retaining vs. non-retaining… (Non-)Linear equation f( ) of several predictive variables Produces continuous range of scores score = f(X 1, X 2, …, X N )

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© Deloitte Consulting, 2004 13 What Powers a Scoring Engine? Scoring Engine: score = f(X 1, X 2, …, X N ) The X 1, X 2,…, X N are as important as the f( )! Why actuarial expertise is necessary A large part of the modeling process consists of variable creation and selection Usually possible to generate 100s of variables Steepest part of the learning curve

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© Deloitte Consulting, 2004 14 Model Evaluation: Lift Curves Sort data by score Break the dataset into 10 equal pieces Best decile: lowest score lowest LR Worst decile: highest score highest LR Difference: Lift Lift = segmentation power Lift ROI of the modeling project

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© Deloitte Consulting, 2004 15 Out-of-Sample Testing Randomly divide data into 3 pieces Training data, Test data, Validation data Use Training data to fit models Score the Test data to create a lift curve Perform the train/test steps iteratively until you have a model youre happy with During this iterative phase, validation data is set aside in a lock box Once model has been finalized, score the Validation data and produce a lift curve Unbiased estimate of future performance

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© Deloitte Consulting, 2004 16 Comparison of Techniques Models built to detect whether an email message is really spam. Gains charts from several models Analogous to lift curves Good for binary target All techniques work ok! Good variable creation at least as important as modeling technique.

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© Deloitte Consulting, 2004 17 Credit Scoring is an Example All of these concepts apply to Credit Scoring Knowledge discovery in databases (KDD) Scoring engine Lift Curve evaluation translates to LR improvement ROI Blind-test validation Credit scoring has been the insurance industrys segue into data mining

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© Deloitte Consulting, 2004 18 Applications Beyond Credit The classic: Profitability Scoring Model Underwriting/Pricing applications Retention models Elasticity models Cross-sell models Lifetime Value models Agent/agency monitoring Target marketing Fraud detection Customer segmentation no target variable (unsupervised learning)

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© Deloitte Consulting, 2004 19 Data Sources Companys internal data Policy-level records Loss & premium transactions Agent database Billing VIN…….. Externally purchased data Credit CLUE MVR Census ….

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© Deloitte Consulting, 2004 The Predictive Modeling Process Early: Variable Creation Middle: Data Exploration & Modeling Late: Analysis & Implementation

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© Deloitte Consulting, 2004 21 Variable Creation Research possible data sources Extract/purchase data Check data for quality (QA) Messy! (still deep in the mines) Create Predictive and Target Variables Opportunity to quantify tribal wisdom …and come up with new ideas Can be a very big task! Steepest part of the learning curve

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© Deloitte Consulting, 2004 22 Types of Predictive Variables Behavioral Historical Claim, billing, credit … Policyholder Age/Gender, # employees … Policy specifics Vehicle age, Construction Type … Territorial Census, Weather …

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© Deloitte Consulting, 2004 23 Data Exploration & Variable Transformation 1-way analyses of predictive variables Exploratory Data Analysis (EDA) Data Visualization Use EDA to cap / transform predictive variables Extreme values Missing values …etc

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© Deloitte Consulting, 2004 24 Multivariate Modeling Examine correlations among the variables Weed out redundant, weak, poorly distributed variables Model design Build candidate models Regression/GLM Decision Trees/MARS Neural Networks Select final model

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© Deloitte Consulting, 2004 25 Building the Model 1. Pair down collection of predictive variables to a manageable set 2. Iterative process Build candidate models on training data Evaluate on test data Many things to tweak Different target variables Different predictive variables Different modeling techniques # NN nodes, hidden layers; tree splitting rules…

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© Deloitte Consulting, 2004 26 Considerations Do signs/magnitudes of parameters make sense? Statistically significant? Is the model biased for/against certain types of policies? States? Policy sizes?... Predictive power holds up for large policies? Continuity Are there small changes in input values that might produce large swings in scores Make sure that an agent cant game the system

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© Deloitte Consulting, 2004 27 Model Analysis & Implementation Perform model analytics Necessary for client to gain comfort with the model Calibrate Models Create user-friendly scale – client dictates Implement models Programming skills are critical here Monitor performance Distribution of scores over time, predictiveness, usage of model... Plan model maintenance

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© Deloitte Consulting, 2004 Modeling Techniques Where Actuarial Science Needs Data Mining

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© Deloitte Consulting, 2004 29 The Greatest Hits Unsupervised: no target variable Clustering Principal Components (dimension reduction) Supervised: predict a target variable Regression GLM Neural Networks MARS: Multivariate Adaptive Regression Splines CART: Classification And Regression Trees

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© Deloitte Consulting, 2004 30 Regression and its Relations GLM: relax regressions distributional assumptions Logistic regression (binary target) Poisson regression (count target) MARS & NN Clever ways of automatically transforming and interacting input variables Why: sometimes true relationships arent linear Universal approximators: model any functional form CART is simplified MARS

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© Deloitte Consulting, 2004 31 Neural Net Motivation Let X 1, X 2, X 3 be three predictive variables policy age, historical LR, driver age Let Y be the target variable Loss ratio A NNET model is a complicated, non-linear, function φ such that: φ(X 1, X 2, X 3 ) Y

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© Deloitte Consulting, 2004 32 In visual terms…

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© Deloitte Consulting, 2004 33 NNET lingo Green: input layer Red: hidden layer Yellow: output layer The {a, b} numbers are weights to be estimated. The network architecture and the weights constitute the model.

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© Deloitte Consulting, 2004 34 In more detail…

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© Deloitte Consulting, 2004 35 In more detail… The NNET model results from substituting the expressions for Z 1 and Z 2 in the expression for Y.

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© Deloitte Consulting, 2004 36 In more detail… Notice that the expression for Y has the form of a logistic regression. Similarly with Z 1, Z 2.

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© Deloitte Consulting, 2004 37 In more detail… You can therefore think of a NNET as a set of logistic regressions embedded in another logistic regression.

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© Deloitte Consulting, 2004 38 Universal Approximators The essential idea: by layering several logistic regressions in this way… …we can model any functional form no matter how many non-linearities or interactions between variables X 1, X 2,… by varying # of nodes and training cycles only NNETs are sometimes called universal function approximators.

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© Deloitte Consulting, 2004 39 MARS / CART Motivation NNETs use the logistic function to combine variables and automatically model any functional form MARS uses an analogous clever idea to do the same work MARS basis functions CART can be viewed as simplified MARS Basis functions are horizontal step functions NNETS, MARS, and CART are all cousins of classic regression analysis

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© Deloitte Consulting, 2004 40 Reference For Beginners: Data Mining Techniques --Michael Berry & Gordon Linhoff For Mavens: The Elements of Statistical Learning --Jerome Friedman, Trevor Hastie, Robert Tibshirani

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