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The Matrix Inverted: A Primer in the Theory of GLMs
CAS Annual Meeting
New Orleans
November 9-12, 2003
Gilbert Korthals, FCAS, MAAA, Assistant Vice President, Actuary
GuideOne Insurance, 515.267.5277, [email protected]
Encounters Along the GLM Path
Preparing for the trip
Modeling curves
Implementation speed bumps
Choosing the Vehicle & Features
Software
Hardware
Driver
Packing the Van
Data collection
Coding
Exposures
Other situations
Data Collection
Amount of data: Minimum 50k to 100k earned exposures
Different sources
Matching records
External data
Sources? Cost? Usability?
Coding Definitions
Thoroughly know your codes Check for reasonableness
Mapping Codes change over time Territory #’s, BI limits
Integrity
How good are the codes?
Still being updated?
Driver/vehicle assignments
Exposures
Balance # of variables and exposures Try to have 50+% of field populated
Re-map smaller exposures
CW vs state specific analysis?
Low frequency exposures
Other Data Situations Treatment of CWP’s
Can model handle severity = 0?
Records with negative amounts Can model handle?
Excess vehicles What driver chars.
do you assign?
Orphan claims
Software
On the Highway - Modeling
Counterintuitive results
Factor categorization
Business decisions
Counterintuitive Results
Interpretation issue
Example - limits & deductibles
Near aliasing
Look at each year to see if pattern consistent
Look at other coverages
Factor Categorization
Categorization Creating a new variable from two or more
other variables – sex and marital status
Myriad of choices & combinations
Need sufficient exposures and claims
Goal is not to find as many combinations as possible
Goal is to find ones too powerful to ignore
Decision Time Considerations
When to change current rates/relativities
How far to change current rates
What new variables to include
Removal of variables impacts interaction among remaining variables
Competition & comparing to existing rates
Competition
Who to look to?
How similar is their rating system to yours?
How similar is their book of business to yours?
Comparing to Competition & Existing Rates
Re-rating book of business
Retention analysis
Leaving money on the table
Know your marketing opportunities
Finalize rating plan Understand impact of
tempering or excluding variables
Managing Market Disruption
No easy answer
To convert or not to convert
Conversion choices Look at matching price points
(assuming you have the data and allowed by regulators)
Allow swings (with or without capping)
Remember credit scoring
Dealing with Other Audiences
Senior management
Underwriting
Systems
Regulators
End of the Road?
Not a once in a lifetime vacation
Fear of breakdowns, detours, squabbling kids and unknown
Questions?Questions?
