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CAS 2008 Spring Meeting
Joint Meeting CIA/SOA/CAS
A Survey of P&C Predictive
Modeling Applications
Gaétan Veilleux, FCAS, MAAA
June 18, 2008
What is Predictive Modeling?
A statistical process which estimates the value of an
observed item (dependent variable) based upon the
values of other explanatory variables.
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P&C Predictive Modeling applications
 Generalized Linear Models (GLM)
 Data mining and other methods
– Artificial neural networks
– Classification and regression trees (CART)
– Multivariate adaptive regression splines (MARS)
– Cluster analysis
– Principal components analysis / factor analysis
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Generalized linear models
E[Y] = m = g-1(X.b + x)
Var[Y] = f.V(m) / w
 Consider all factors simultaneously
 Allow for nature of random process
 Provides diagnostics
 Robust and transparent
 Increasingly a global standard
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Insurance applications of GLMs









Ratemaking
Underwriting
Marketing
Retention
Expense analysis
Claims management
Risk management / reinsurance
Sales channel
Reserving
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Applications
 Ratemaking
– Revise existing rating factor relativities with
multivariate analysis
– Introduce new rating variables or underwriting tiers
– Re-define territorial boundaries
– Re-define vehicle classifications
– Unbundle homeowners by-peril
– Understand effect of proposed rate changes at
renewal (including moderator algorithms)
– Define rating plan that optimizes profit while retaining
required volume
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Ratemaking objective
Age
Sex
Vehicle
Rating Plan
Premium
Area
Claim
Limit
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Modeling the cost of claims
Age
Sex
Vehicle
Area
Model
Expected
cost of
claims
Claim
Limit
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Modeling the cost of claims
BI
Freq
x
Amt
= Cost 1
PD
Freq
x
Amt
= Cost 2
MED Freq
x
Amt
= Cost 3
COL
Freq
x
Amt
= Cost 4
OTC
Freq
x
Amt
= Cost 5
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GLM output (significant factor)
1.2
200000
180000
1
154%
138%
0.8
160000
105%
140000
84%
73%
0.6
120000
72%
58%
100000
45%
0.4
39%
80000
31%
Exposure (years)
Log of multiplier
93%
60000
0.2
5%
40000
0%
0
20000
-0.2
0
1
2
3
4
5
6
7
8
9
10
11
12
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Vehicle symbol
P value = 0.0%
Onew ay relativities
Approx 95% confidence interval
Parameter estimate
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Age - sex interaction
Example job
Run 5 Model 3 - Small interaction - Third party material damage, Numbers
1
155%
138%
300000
0.8
250000
63%
63%
46%
0.4
200000
40%
28%
19%
24%
20%
150000
0.2
13%
Exposure
Log of multiplier
0.6
6%
0%
-2%
100000
-6%
0
-11%
-18%
-19%
-0.2
50000
-0.4
0
17-21
22-24
25-29
30-34
35-39
40-49
50-59
60-69
70+
P level = 0.0%
Rank 6/6
Age of driver.Sex of driver
Approx 2 SEs from estimate, Sex of driver: Female
Approx 2 SEs from estimate, Sex of driver: Male
Unsmoothed estimate, Sex of driver: Female
Unsmoothed estimate, Sex of driver: Male
Smoothed estimate, Sex of driver: Female
Smoothed estimate, Sex of driver: Male
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Impact analysis
Example job
Age of driver
7000
180%
170%
160%
6000
150%
140%
5000
120%
4000
110%
100%
3000
Loss ratio
Count of records
130%
90%
80%
2000
70%
60%
1000
50%
40%
0
30%
0.450 0.500
0.600 0.650
0.750 0.800
0.900 0.950
1.050 1.100
1.200 1.250
1.350 1.400
1.500 1.550
1.650 1.700
1.800 1.850
1.950 2.000
2.100 2.150
2.250 2.300
2.400 2.450
Ratio: Risk Premium / Current premium
tariff
17-21
22-24
25-29
30-34
35-39
40-49
50-59
60-69
70+
Claims / Earnedprem
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Applications
Underwriting
– Provide guidelines on debits/credits
– Produce scorecards to automate some elements of
risk selection
Marketing
– Improve direct mail conversion rate for most profitable
risks
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Scoring
Distribution of score
2500
160%
140%
2000
100%
1500
80%
1000
60%
Actual loss ratio
Number of policies
120%
40%
500
20%
0
0%
0
2 4
6
8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 52 54 56 58 60 62 64 66 68 70 72 74 76 78 80 82 84 86 88 90 92 94 96 98 100
Score based on expected loss ratio
Number of policies
Actual loss ratio
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Applications
 Retention
– Understand effect of capping rate changes at renewal
– Develop lifetime customer value model
 Expense analysis
– Vary acquisition costs by other criteria
 Claims management
– Develop fraud scorecard
– Advise how TPAs affect claim costs
– Analyze the drivers of claim cost and hence loss
control
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Applications
Risk management / reinsurance
– Determine which risks to cede
Sales channel
– Align compensation with expected profitability
Reserving
– Provide additional method to assist reserving
actuaries with ultimate projections
– Identify predictors of “serious” claims
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P&C Predictive Modeling applications
 Generalized Linear Models (GLM)
 Data mining and other methods
– Artificial neural networks
– Classification and regression trees (CART)
– Multivariate adaptive regression splines (MARS)
– Cluster analysis
– Principal components analysis / factor analysis
17
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Data Mining





aka Knowledge Discovery in Databases (KDD)
Broad range of methods
Good at discovery, weak at estimation
Many (most) are not being applied to P&C insurance
ACM SIGKDD International Conference on
Knowledge Discovery & Data Mining
– Evolutionary spectral clustering by incorporating temporal smoothness
– Making generative classifiers robust to selection bias
– Nonlinear adaptive distance metric learning for clustering
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Data Mining – 5 Common Techniques
 Artificial neural networks
– Non-linear predictive models that learn through
training
– Resemble biological neural networks in structure
 Decision trees
– Tree-shaped structures that represent sets of
decisions
– These decisions generate rules for the classification
of a dataset
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Data Mining – 5 Common Techniques (2)
 Genetic algorithms
– Optimization techniques
– Genetic combination, mutation, and natural selection
 Nearest neighbor
– Classification of each record based on a combination
of the classes of the k record(s) most similar to it in a
historical dataset
 Rule induction
– Extraction of useful if-then rules from data based on
statistical significance
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Artificial Neural Networks
 ID
–
–
–
structural components for a GLM
Variables
Binning
Interactions
Input
Hidden
Output
 Fraud detection
– Staged accidents
– Other PM techniques
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Classification and Regression Trees - CART





Decision tree based method
Binary recursive partitioning
Brute force non-parametric method
Response is discontinuous
Doesn’t capture strong linear relationships well
N = 100,000
Applications
 Variable selection
 Binning
 Identify predictors of “serious” claims
Area = {1, 2, 3}
Area = {others}
N = 41,127
N = 58,873
Density <50
Density >100
N = 11,245
N = 2,743
Density 50-100
N = 44,885
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Multivariate Adaptive Regression Splines MARS




Multivariate non-parametric regression procedure
Brute force
Response is continuous
Piece-wise linear segments to describe non-linear
relationships
Applications
 Variable selection
 Binning
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Cluster Analysis




Seek to identify homogeneous subgroups
Average linkage or centroid methods
No good literature explaining which is best
Minimize within-group variation and maximize
between-group variation
Applications
 Vehicle symbols
 Segmenting/Tiering
 Fraud detection
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Principal Components/Factor Analysis
 Reduce number of variables
 Detect structure
 Consecutive factors are independent of (orthogonal
to) each other
Applications
 Economic models s/a trend
 Transform/reduce variables
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ISO Innovative Analytics - Risk Analyzer
Modeling Techniques Employed
 Variable Selection – univariate analysis, transformations, known




relationship to loss
Sampling
Regression / general linear modeling
Sub models/data reduction – neural nets, splines, principal
component analysis, variable clustering
Spatial Smoothing – with parameters related to auto insurance
loss patterns
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Quotes
“Prediction is very difficult, especially if it's about
the future.”
- Nils Bohr, Nobel laureate in Physics
"I have seen the future and it is very much like the
present, only longer."
- Kehlog Albran, The Profit
"A good forecaster is not smarter than everyone
else, he merely has his ignorance better
organized."
- Anonymous
27
Copyright © Watson Wyatt Worldwide. All rights reserved
watsonwyatt.com
CAS 2008 Spring Meeting
Joint Meeting CIA/SOA/CAS
A Survey of P&C Predictive
Modeling Applications
Gaétan Veilleux, FCAS, MAAA
June 18, 2008