Download - PREDICTIVE MODELS IN LIFE INSURANCE
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PREDICTIVE MODELS IN LIFE
INSURANCE
Philip L. Adams, ASA, MAAA
Date: 17 June 2010
Agenda
1. Predictive Models Defined
2. Predictive models past and present
3. Actuarial perspective
4. Application to Life Insurance: ILEC 02-04 and 05-07 data
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PREDICTIVE MODELS
WHAT THEY ARE (AND AREN’T)
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What is predictive modeling?
“Predictive modeling is the use of modern statistical methods to identify and
measure past associations for the sake of inferring associations about the past, the
present and the future. Usually, this is expressed through probabilities, and it has a
very strong Bayesian flavor.”
-Your humble speaker
This sounds a lot like what actuaries have been doing for a century (except for the
“modern statistical methods” part).
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What it’s not
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Panacea Best thing since sliced
bread
The tool to end all tools
Nuts and Bolts of Predictive Modeling
Data mining: Use statistical methods to find patterns
“Correlation does not imply causation”
…but we often have to assert causation
Some associations cannot be measured using correlation
Correlation is measure of statistical collinearity
Correlation implies dependency, but not conversely
Example: If X is uniform on (-1,1), then X2 is uncorrelated with X
Take action with those patterns
Build a better product or service
Incorporate into risk management
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PREDICTIVE MODELS
PAST AND PRESENT
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PREDICTIVE MODELS: The PastHoroscopes
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PREDICTIVE MODELS: In FictionThe Witch in Monty Python’s Holy Grail
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“Experience” taught
knight that witches
float, so compare
candidate to other
things that float
Peasants’ suggested
comparisons: wood,
very small rocks,
churches, water fowl
Analogous to a
decision tree
PREDICTIVE MODELS: Real Data, Bad AnalysisPirates and Global Warming
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Number of
pirates has
decreased since
1860
Globe has
consistently
warmed
Ergo, Somalia is
at the forefront
of the fight
against global
warming
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PREDICTIVE MODELS: Dubious conclusions
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More pirates!
PREDICTIVE MODELS: The Present
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Mortality tables
Lapse tables
Trends
Credit scoring
Underwriting manuals
UCS
Fraud detection
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Manual, ad hoc
Inefficient use of data
Inefficient models
Modeler biases strong (often hidden)
…but gets the job done
Formal, statistically sound systems
Extracts a lot of information
Models efficiently capture relationships
Modeler biases must be explicit
…remains mysterious
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Comparisons
Life Actuarial Modeling Predictive Modeling
Whitaker-Henderson Graduation
Analysis of A/E ratios
Underwriting rules
Credibility (basic)
Additive models with splines
Regression models with offsets
Decision trees
Credibility (advanced)
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Analogues
Life Actuarial Modeling Predictive Modeling
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APPLICATIONS TO LIFE INSURANCE
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Modeling the ILEC 02-04 Data
• Death claims and exposures on fully underwritten lives from 35 companies
collected between 2002 and 2004
• Nearly 700,000 claims overall
• Almost 500,000 in durations 21+
• For this presentation, we confine our attention to a particular subset
• Attained ages 20-84, durations 1-10
• Face amounts at least $10,000 and summarized into two bands
• Left with 37,087 death claims
• We anchor to PPR ultimate model from Edwalds, Craighead, Adams paper
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Modeling the ILEC 02-04 Data
Modeling with GAMs
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Linear Model
• Standard regression model using least squares minimization of some response against some collection of predictor variables
Generalized Linear Model
• Expand universe of response variables to probabilities, counts, etc.
Generalized Additive Model
• Expand universe of predictors to include smooth functions
xy 10
xyg 10
xfyg 0
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Modeling with GAMs
Splines underly “smooth functions”
Cubic splines
Penalized splines
Thin-plate regression splines
Tensor product splines
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Fitting GAMs to ILEC 02-04:
Non-smoker Surface
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Fitting GAMs to ILEC 02-04:
Smoker Surface
Fitting GAMs to ILEC 02-04:
Model Parameters
Parameters (offset from ultimate) Estimate Std. Error p-value e.d.f.
Fixed
Intercept -0.317 0.062 0.00% 1
Males -0.059 0.012 0.00% 1
Face Amounts $50,000+ -0.399 0.012 0.00% 1
Non-smokers -0.298 0.062 0.00% 1
Smokers 0.488 0.065 0.00% 1
Non-smokers in Duration 1 -0.823 0.078 0.00% 1
Non-smokers in Duration 2 -0.199 0.039 0.00% 1
Smokers in Duration 1 0.000 1
Smokers in Duration 2 -0.173 0.055 0.16% 1
SmoothNon-smokers 63 parameters 0.00% 18.06
Smokers 63 parameters 0.00% 9.81
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Fitting GAMs to ILEC 02-04:
Smoker Penalty
But can it predict?
Attach to ILEC 05-07 Dataset
Confined to data similar to fitting set
Data summarized, so judgment used for choice of age and duration
Table projected forward to 2008 using 1% per annum flat
Compare to 2008 VBT
Represents actuarial approach
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2008 VBT and GAM ComparedGender and Smoker Status
A/E by Count A/E by Amount
Claims 08VBT Primary Predictive Model 08VBT Primary Predictive Model
Female 11,402 110.1% 112.8% 95.4% 105.9%
Non-Smoker 8,812 108.8% 110.1% 95.9% 105.3%
Smoker 2,590 115.1% 123.1% 92.4% 109.9%
Male 20,654 107.8% 106.6% 87.1% 88.2%
Non-Smoker 15,663 106.3% 105.0% 86.4% 86.9%
Smoker 4,991 113.1% 112.0% 92.1% 96.7%
Overall 32,056 108.7% 108.7% 89.2% 92.3%
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Bottom line results are comparable.
2008 VBT and GAM ComparedFace Amount Band
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A/E by Count A/E by Amount
Claims 08VBT Primary Predictive Model 08VBT Primary Predictive Model
10,000-24,999 4,062 150.7% 121.8% 149.7% 120.5%
25,000-49,999 4,212 135.5% 106.6% 134.9% 106.2%
50,000-99,999 5,531 121.4% 136.6% 120.7% 135.9%
100,000+ 18,251 95.3% 100.6% 87.0% 90.3%
Overall 32,056 108.7% 108.7% 89.2% 92.3%
GAM has better control for face amount variation.
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2008 VBT and GAM ComparedAttained Age Slope
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2008 VBT and GAM ComparedDuration Slope
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References
Edwalds, T., Craighead, S., Adams, P. (2008) “Estimating Mortality Risk Using
Predictive Modeling.” Enterprise Risk Management Symposium.
Lowrie, Walter B. (1982) “An Extension of the Whittaker-Henderson Method of
Graduation,” Transactions of the Society of Actuaries, Vol. 34, pp. 329-372
R Development Core Team (2009). R: A Language and environment for
statistical computing. Vienna, Austria. R Foundation for Statistical Computing
Wood, S. (2006) Generalized Additive Models: An Introduction with R. Chapman
& Hall, London.
Image Credits
• Wikimedia Commons
• Monty Python
• Veganza.com
• Wenger
• CDC
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