Predictive Modeling GLM and Price Elasticity Model. David Dou October 8 th, 2014

Transcription

1 Predictive Modeling GLM and Price Elasticity Model David Dou October 8 th, 2014

2 History of Predictive Modeling Pre-Computer Era: Triangles on a giant spreadsheet PC Era: Microsoft Excel oneway relativities Later part of PC Era: multivariate analysis (imagine the following analysis involving all age buckets, vehicle values, other continuous variables, became impossible to estimate accurately) Loss Premium Loss Ratio Ratio Male 750 1, Female 500 1, Total 1,250 2, Loss Premium Loss Ratio Ratio Single 833 1, Married 417 1, Total 1,250 2, Single Male Single Female Married Male Married Female Straight Multiplying Actual Ratio

3 Goals of Predictive Modeling Two Main Goals: Price accurately Discover new rating variables Case Study: Legislature of Michigan, a liberal state, voted to allow insurance companies to price more freely, openly, and in line with actual loss propensity in soon, other bureau followed. Progressive started to use personal credit score in personal automobile insurance rating plan in 1997 in Michigan. By 2000, 31 companies in all 50 states are using some forms of personal credit score to guard against adverse selection. Credit Score Num of Quote Indicated Charged Others , , , , , ,

4 Why Generalized Linear Model What is ordinary linear Model Predicting Y using X s, assuming error distribution is normal Simple linear regression: Estimating MPG using Vehicle Weight: Y = a + bx + u Where: Y= Miles Per Gallon X= Vehicle Weight a= the intercept b= the slope u= the regression residual 4

5 Why Generalized Linear Model Multiple linear regression: Estimating MPG using Horsepower, vehicle weight, vehicle height, etc: Y = a + b1x1 + b2x2 + b3x3 + + u 5

6 Why Generalized Linear Model What is generalized Linear Model: flexible generalization of ordinary linear regression that allows for response variables that have error distribution from a particular distribution in the exponential family: Normal Binomial Poisson Gamma others Utilizing a link function to standardize the regression process. 6

7 Statistical Considerations Homogeneity coverage cannot be too much different Credibility need to have enough data for each variables Predictive Stability too finely-tuned model can be overfitting Model Suitability Make sure frequency/severity is exhibiting the right distribution 7

8 Generalized Linear Model Assumption Frequency Model Usually assume Poisson distribution P is the probability of observing x events in the interval u is the average number of events that occur in the interval In P&C insurance term, the interval is usually one year Modeling can be seen as a machine learning exercise to estimate the u. once we know the parameter, we can estimate the claim frequency 8

9 Generalized Linear Model Assumption Severity Model Usually assume Gamma distribution Pay attention to artificial bipolarity in Gamma distribution In P&C insurance term, we estimate the severity of the claim once a claim happens Modeling can be seen as a machine learning exercise to estimate the a (shape parameter and b (scale parameter). One we know the shape and scale parameter, we can estimate the future severity of a claim 9

10 Why Generalized Linear Model Loss Ratio Model Assumes Lognormal distribution Needs extensive work on Premium on-leveling and premium adequacy analysis Utilizing Tweedie Distribution Pure Premium Model include the purely continuous gamma distribution, the purely discrete scaled Poisson distribution, and the class of mixed compound Poisson gamma distributions which have positive mass at zero, but are otherwise continuous 10

11 Pure Premium Model Advantage over Loss Ratio Model 1 Less Assumption No need to use Premium thus no premium on-level, adequacy issue No need to consider insurance cycle hard and soft market is no diffe 2 Other Model/Analysis can use the pure premium (because it has direct monetary impact) Marketing Analysis Underwriting Model Customer Lifetime value analysis 11

12 Generalized Linear Model Advantage Accurate Pricing Making Pricing More competitive Discover important variables Increase profitability Reflect true cost of the risk Elasticity, Lifetime Value Understand renewal retention Understand cross-sale propensity Discover customer lifetime value Underwriting risk Underwrites the correct risks Analyze profitability of risks Customer segmentation Assist in targeting correct risks Market / Claim Model Increase market response rate Increase sales conversion Estimate claim fraud Early warning for claim department 12

13 What is Elasticity Model 1 Goal A tool to enable actuaries to estimate underwriting profit at different levels of price change so we can maximize profit or maximize premium 2 Why We Model Elasticity Gain a better understanding of the marketplace Collect extra premium when below market price Price more aggressively to retain profitable business Identify profitable niches for new business Gain insight into how price changes affect performance Realize a sustainable increase in profitability 13

14 How Elasticity Model is used Model Building Y = a + bx1 +cx2 + dx3 + + jx9 + u Where: Y= Renewal (0 = lapse; 1 = renew) X1= Price Change b= coefficient for Price Change model is fitted on historical renewal retention for individual policies with different premium increases on renewal Expected Renewal % Policy Number Predicted Renewal % Price Change Age Gender Current Premium Expected Premium % 43 M $ 1,000 $ % 24 F $ 1,400 $ 1, % 22 M $ 1,700 $ 1,346 Total $ 4,100 $ 3,590 Policy Number Predicted Renewal % Price Change Age Gender Current Premium Expected Premium % 43 M $ 1,000 $ 1, % 24 F $ 1,400 $ 1, % 22 M $ 1,700 $ 1,466 Total $ 4,100 $ 3,918 Policy Number Predicted Renewal % Price Change Age Gender Current Premium Expected Premium % 43 M $ 1,000 $ % 24 F $ 1,400 $ 1, % 22 M $ 1,700 $ 1,464 Total $ 4,100 $ 3,734 14

15 Predictive Modeling GLM and Price Elasticity Model Questions? 15