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

Synopsis Better mortality models needed Especially preferred mortality SoA 2002-04 dataset presents opportunity Projection Pursuit Regression does it! Modeling approach Model results Testing the model

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 2002-03 and 2003-04 annual studies

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

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

PPR

PPR Predictor

PPR Projection

PPR Ridge Function

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

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

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)

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

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

Questions? Thank You!