1. Similarity Modeling Chuck Boucek
Insurance and Actuarial Advisory Services
Similarity Modeling
Chuck Boucek
CAS Seminar on Predictive Modeling – Las Vegas, Nevada October 11 – 12,

2. Agenda Overview Underwriting Model Similarity Model Market Deployment
Conceptual framework
Process
Model results
Market Deployment

3. Overview Company’s book of business is a function of its
Target market
Underwriting practices
Location of agencies
Underwriting model is based on company’s own data
Model is sometimes employed to score risks outside of target market
Company approaches to addressing policyholders at extremes of historical data
Limits on risks that are scored via model
Manual underwriting of selected groups
Modeling approach
(Continued)

4. Overview Business risks of predictive modeling
Model does not appropriately assess policyholders
Model deployment worsens policyholder retention
Model is inappropriately extrapolated to policyholders
Can an underwriting model be used to score all potential policyholders?
How to treat policyholders at extremes of historical data?
Is there a structured way of assessing how similar a policyholder is to the policyholders in the data used to build the model?

5. Underwriting Model – Lift Chart
1.4
1.4
Predicted
Actual
1.3
1.3
1.2
1.2
1.1
1.1
Relative Frequency
1.0
1.0
0.9
0.9
0.8
0.8
0.7
0.7
0.6
Source of all graphs: Ernst & Young Insurance and Actuarial Advisory Services
0.6
(Continued)

6. Underwriting Model – Predictor Variable #1
Credit Variable
0.0
0.2
0.4
0.6
0.8
1.0
2,000
4,000
6,000
8,000
10,000
1.2
1.4
1.6
1.8
2.0
Relative Frequency
Underwriting Model – Predictor Variable #1
2 SE
Number of Observations
# Observations
(Continued)

7. Underwriting Model – Predictor Variable #2
2.0
60,000
1.8 A
1.6
2 SE
Number of Observations
40,000
Relative Frequency
# Observations
1.4 B
1.2
20,000 C
1.0
0.8 A B C
Internal Class Variable
Internal Class Variable

8. Similarity Model Conceptual framework
Policyholders with greater certainty in the claim frequency prediction should score higher
Generally, there is greater uncertainty in predictions from areas with more sparse data
Want to be able to assess similarity in a multivariate framework
(Continued)

9. Similarity Model Process
Generate one record for every record in modeling database
Numeric variable will be from a uniform distribution over the range of actual values
Factor variable will have an equal frequency for each level of the factor
Variables are limited to those in underwriting model
Create an indicator variable
1 = Record is from actual data
0 = Record is from generated data
Perform a logistic regression with the indicator variable as response variable
Response variable assumed to be binomial
Logit link function
(Continued)

10. Similarity Model – Predictor Variable #1
Credit Variable: Indicator = 1
0.0
0.2
0.4
0.6
0.8
1.0
2,000
4,000
6,000
8,000
10,000
Credit Variable: Indicator = 0
Similarity Model – Predictor Variable #1
# Observations
# Observations
Number of Observations
Number of Observations
(Continued)

11. Similarity Model – Predictor Variable #2
60,000
60,000
Number of Observations
Number of Observations
# Observations
# Observations
40,000
40,000
20,000
20,000 A B C A B C
Internal Class Variable: Indicator = 1
Internal Class Variable: Indicator = 0
(Continued)

12. Similarity Model Results – Average Scores
50,000
0.98
40,000
# Observations
30,000
Number of Observations
20,000
10,000
0.88
0.8
0.75
0.66
0.65
0.56
0.55
0.63
0.59
0-0.1
0.9-1
(Continued)
Credit Variable

13. Similarity Model Results – Average Scores
0.95
60,000
40,000
# Observations
Number of Observations
0.92
20,000
0.8 A B C
(Continued)
Internal Class Variable

14. Similarity Model – Summary
Advantages of this process
Produces results consistent with desired characteristics
It is a structured way of sorting risks from the fringes of the distribution
It is straightforward conceptually
It employs a Generalized Linear Model
This is not the only process that can be employed
(Continued)

15. Similarity Model – Impact on Lift Chart
Similarity Decile 10
1.6
1.6
Predicted
Actual
1.4
1.4
1.2
1.2
Relative Frequency
1.0
1.0
0.8
0.8
0.6
0.6
(Continued)
0.4
0.4

16. Similarity Model – Impact on Lift Chart
Similarity Decile 2
1.6
1.6
Predicted
Actual
1.4
1.4
1.2
1.2
Relative Frequency
1.0
1.0
0.8
0.8
0.6
0.6
(Continued)
0.4
0.4

17. Similarity Model – Impact on Lift Chart
Similarity Decile 1
1.6
1.6
Predicted
Actual
1.4
1.4
1.2
1.2
Relative Frequency
1.0
1.0
0.8
0.8
0.6
0.6
(Continued)
0.4
0.4

18. Similarity Model Observations
Policyholders in similarity decile 1 should show more variability in actual results
The predicted spread in claim frequency is smaller in decile 10 than in decile 1
The policyholders in decile 10 tend to be alike

19. Market Deployment Applications Select a cutoff similarity score
Based on variability in lift chart
Professional judgment of underwriting staff
Policyholders with lower similarity scores will receive greater underwriting attention
Monitor results by similarity group