1. Mortality Modeling using Projection Pursuit Regression
Tom Edwalds, Munich American Reassurance Company
Steve Craighead, Towers Perrin

2. Synopsis Better mortality models needed
Especially preferred mortality
SoA dataset presents opportunity
Projection Pursuit Regression does it!
Modeling approach
Model results
Testing the model

3. The Opportunity
Insurers want new rules for preferred mortality valuation
SoA Individual Life Experience Committee (ILEC) promised preferred mortality study
Contingent on data collected for and annual studies

4. SoA ILEC 2002-04 Dataset Great response to call for data
35 companies
75 million life-years exposed
700,000 deaths
sex, age, duration, smoking status
New data elements requested
9 face amount bands
Risk class rank
Product type

5. Our Quest
To learn as much as possible from this dataset about current mortality
Using modern statistical tools
Data mining
Predictive modeling
Generalized Linear Models
Generalized Additive Models
Projection Pursuit Regression (PPR)
Chose PPR

6. PPR

7. PPR
Predictor

8. PPR
Projection

9. PPR
Ridge
Function

10. Data Quirks No smoker info after duration 24
70% of deaths after duration 25
Risk class info on 4% of data
Product type field unreliable

11. Modeling Strategy Construct ultimate duration unismoke model
By gender, attained age, face amount band
Durations 26+ for ages under 90
Durations 3+ for ages 90+
Then durations 1-25, ages under 90
Add smoker status, more bands

12. Modeling Decisions Compress ultimate data so highest band is $25K +
Predict A/E by policy vs 2001 VBT
Set bounds for q(x)
Compress select data so highest band is $500K +
Predict A/E by policy vs ultimate PPR model
Set bounds for q(x,t)

26. Measuring Model Fit Compare actual to predicted deaths by cell
Predicted deaths = model q * exposures
Use two-sided Poisson test
1 – Pr{# deaths closer to mean than actual}
# deaths must be integer

29. Next Steps Refine ultimate models Regenerate PPR select models
Investigate effect of preferred classes

30. Questions?
Thank You!