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**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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**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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**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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**Semantics: DM vs PM Data exploration techniques (some brute force)**

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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**Strategy: Why do Data Mining?**

Think Baseball!

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Bay Area Baseball In 1999 Billy Beane (manager for the Oakland Athletics) found a novel use of data mining. Not a wealthy team Ranked 12th (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 A’s ranked 2nd!

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**Implication Beane quantified how well a player would do. Implication:**

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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**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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**Keeping Score Billy Beane CEO who wants to run the next Progressive**

Beane’s Scouts Underwriter Potential Team Member Potential Insured Bill James’ stats Predictive variables – old or new (e.g. credit) Billy Bean’s number cruncher You! (or people on your team)

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**What is Predictive Modeling?**

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**Three Concepts Scoring engines Lift curves Out-of-sample tests**

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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**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(X1, X2, …, XN)

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**What “Powers” a Scoring Engine?**

score = f(X1, X2, …, XN) The X1, X2,…, XN 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 100’s of variables Steepest part of the learning curve

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**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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**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 you’re 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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**Comparison of Techniques**

Models built to detect whether an 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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**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 industry’s segue into data mining

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**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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**Data Sources Company’s internal data Externally purchased data**

Policy-level records Loss & premium transactions Agent database Billing VIN…….. Externally purchased data Credit CLUE MVR Census ….

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**The Predictive Modeling Process**

Early: Variable Creation Middle: Data Exploration & Modeling Late: Analysis & Implementation

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**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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**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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**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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**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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Building the Model Pair down collection of predictive variables to a manageable set 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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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 can’t game the system

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**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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**Where Actuarial Science Needs Data Mining**

Modeling Techniques Where Actuarial Science Needs Data Mining

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**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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**Regression and its Relations**

GLM: relax regression’s 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 aren’t linear Universal approximators: model any functional form CART is simplified MARS

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**Neural Net Motivation Let X1, X2, X3 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(X1, X2, X3) ≈ Y

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In visual terms…

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**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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In more detail…

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In more detail… The NNET model results from substituting the expressions for Z1 and Z2 in the expression for Y.

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In more detail… Notice that the expression for Y has the form of a logistic regression. Similarly with Z1, Z2.

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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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**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 X1, X2,… by varying # of nodes and training cycles only NNETs are sometimes called “universal function approximators”.

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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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**Reference For Beginners: For Mavens: Data Mining Techniques**

--Michael Berry & Gordon Linhoff For Mavens: The Elements of Statistical Learning --Jerome Friedman, Trevor Hastie, Robert Tibshirani

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