2. ®
“Predictive Modeling:
Pricing Service Contracts
in a Competitive
Environment”
Mike Paczolt, FCAS, MAAA
Consulting Actuary
Milliman
3. About Milliman ®
• Actuaries and other consultants
• Independent – Not broker or insurance carrier
• Over 2,100 Employees
• Offices in most major cities globally
4. Adverse Selection – Year 1 ®
PRICE
Low Risk High Risk
Company A $25 $75
Company B $50 $50
# of Policies
Low Risk High Risk
Company A 1,000 1,000
Company B 1,000 1,000
Company B – Profit Summary
Low Risk High Risk
Profit Per Policy +$25 -$25
# Policies x 1,000 x 1,000
Total Profit +$25,000 -$25,000
6. Adverse Selection – Year 2 ®
PRICE
Low Risk High Risk
Company A $25 $75
Company B $50 $50
# of Policies
Low Risk High Risk
Company A 1,500 500
Company B 500 1,500
Company B – Profit Summary
Low Risk High Risk
Profit Per Policy +$25 -$25
# Policies x 500 x 1,500
Total Profit +$12,500 -$37,500
7. Adverse Selection – Year 3 ®
PRICE
Low Risk High Risk
Company A $25 $75
Company B $50 $50
# of Policies
Low Risk High Risk
Company A 2,000 0
Company B 0 2,000
Company B – Profit Summary
Low Risk High Risk
Profit Per Policy +$25 -$25
# Policies x0 x 2,000
Total Profit $0 -$50,000
8. 2 Types of Pricing Analysis ®
Cost Per Exposure Predictive Modeling
• High level analysis • Identifies patterns in
data
• Average historical cost
per policy • Captures relationship
between claims and
• Often segmented by policy characteristics
product type
• Accounts for
correlation between
policy characteristics
9. Why use Predictive Modeling? ®
Pricing Develop accurate rates to maintain
profitability and competitiveness
Underwriting Prioritize business for underwriting scrutiny
Sales Target profitable customer base for new
and renewal business
Loss Control Identify root causes of product failures for
quality control
Claims Set thresholds for determining acceptable
Management claim severities
Customer Target highly profitable business for
Management renewals based on lapse rates
10. Probability is a function of… ®
Family
Age Lifestyle Disease
History
On-base Slugging Baseball
ERA
% % Wins
Extended
Product
Supplier Dealer Warranty
Age
Claims
• Predictive modeling attempts to convert these
tendencies into a mathematical formula
11. Predictive Models ®
• One-Way Linear Regression
• Multivariate Linear Regression
• Market Segmentation
• Other advanced techniques are becoming
more popular (e.g. machine learning, price
optimization, etc.)
12. Variables ®
• Location – Zip Code
• Brand/Product Type
• Dealer/Salesman
• Factory
• Product Age/Usage
• Manufacturer/Supplier
• Parts/Components
• Customer Demographics
• Service Level
13. One-Way Regression Example ®
$160 Cost Per Unit by Product Age
$140
$120
Cost Per Unit
$100
$80
$60
$40
$20
$0
0 1 2 3 4 5 6 7 8
Product Age (Years)
14. Inter-Dependencies ®
Supplier X
55%
45% 85%
125%
Customer
Credit Score 90% Sold in IL
<300
85% 75%
15. Multivariate Linear Regression
Example ®
Cost Per Unit by
Product Age & Supplier
$200
$150
$150-$200
$100 $100-$150
$50-$100
$50 $0-$50
D
$0 C
0 1 B Supplier
2 3 A
4 5 6 7
Product Age (Years) 8
16. Market Segmentation
How does it work? ®
Dealer 1
Brand A
4,000 Policies
Brand A
7,500 Policies
Dealer 2
Brand A
Initial Population 3,500 Policies
10,000 Policies
Dealer 1
Brand B
1,500 Policies
Brand B
2,500 Policies
Dealer 2
Brand B
1,000 Policies
18. Building a Predictive Model ®
Implementation
• Pricing
Model • Underwriting
Decisions
• Create Model
• Validate Model
Data
• Gather Data
• Prepare Data
19. Data Gathering ®
• Sales / Policy Database
• Location, supplier, product type, etc…
• Claims Database
• Number of claims by type, claim values amounts
labor/parts, etc…
• External Database
• Credit score, customer purchase history, etc…
20. Data Prep ®
• Clean data is crucial
• May exclude suspect data
• Not uncommon to eliminate 10% to 25% of records
• Data can be held back to validate model
21. Create Model ®
• Decide purpose of model
• Claim Frequency
• Claim Severity
• Loss Ratios
• CPU
• Iterative process
• Use one-way analysis to identify important variables
• Group variables together
22. Model Validation ®
• Monitor “best fit” based on stats
• Correlation vs. Causality
• Back-testing on holdout sample
23. Predictive Modeling Results ®
• Sophisticated statistical model identifying key traits of
claims that answers:
• What segments of my portfolio am I making
money?
• What is my price floor?
• Are certain dealers/salesman underperforming
peers?
• What is causing my warranty claims?
• Should I reduce or expand coverage?
• Which customers should my sales team target?
24. Sample Results
Underwriting Purpose ®
Loss Ratio by Segment
150%
125%
Loss Ratio
100%
75%
50%
25%
1 2 3 4 5 6 7 8 9 10
Segment
25. Sample Results
Rating Plan ®
Base Rating
Product Wholesale Price Rate Policy Length Factor
<$1,000 $200 1 Year 1.00
$1,001 to $10,000 $300 2 Year 1.90
>$10,000 $1,000
Rating Rating
Product Age Factor Renewal Factor
< 1 Year 1.00 No 1.00
1 Year to 5 Years 1.20 Yes 0.95
> 5 Years 2.00
26. Sample Results
Sales Purpose ®
Loss Ratio vs.
Relative SC Revenue Growth
150%
125%
Loss Ratio
100%
75%
50%
25%
-10% -5% 0% 5% 10%
Relative Service Contract Revenue Growth
