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Determination
of
Geographical Territories
by
Michael J. Miller
EPIC Consulting, LLC
2004 CAS Ratemaking Seminar
Risk Classification
Definition –
A grouping of risks with similar risk
characteristics so that differences in costs
may be recognized.
Purpose –
Means by which data can be gathered so as
to measure and quantify a specific risk
characteristic’s relation to the propensity for
loss.
Example –
Territory classes are a means to gather data
so as to measure and quantify geographic
risk factors relative to the propensity for loss.
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Homogeneity
Definition –
A risk classification is homogeneous if all
risks in the class have the same or similar
degree of risk with respect to the specific risk
factor being measured.
Purpose –
Homogeneity of the class increases the
credibility of the loss data generated by the
class.
Example –
A territory is considered homogeneous if all
risks in the territory represent the same, or
approximately the same, geographical risk.
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Statistical Test of Homogeneity
Within Variance: Based on the squared difference between each zip code pure
premium in the cluster and the average pure premium for the specific
cluster being tested
Between Variance: Based on the squared difference between each cluster’s
pure premium and the statewide average pure premium
Total Variance = Within Variance + Between Variance
Within Variance Percentage = Within Variance divided by Total Variance
Goals: Low Percentage of Total Variance Within
High Percentage of Total Variance Between
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Basis to Group Areas
County
• Largely stable over time
• Broad area
ZIP Code
• Narrowly defined may be beneficial to define territories
• Useful for online rating
• Main disadvantage is need to deal with change over time
Geo Coding
• Finest detail
• Static over time
• No predefined grouping
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Loss Indice
Normalized Pure Premium
Normalized Zip Code Pure Premium
EQUALS
State Ave. Prem.
State Ave. Base
÷
Zip Ave. Prem.
Zip Base
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Loss Indice
Econometric Model
• Population Density
• Vehicle Density
• Accidents per Vehicle
• Injuries per Accident
• Thefts per Vehicle
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Credibility
• 3000 Claims
• Complement
– Neighborhood Pure Premium
– Within Two Miles
– One Mile Extension
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Additional Credibility Considerations
Distance formulas
• Discrete
• Continuous
Choice of complements
• Use of distance based criteria
• Data grouped based on population density groups
• Combination of both distance based and population density
• Entire state
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Sigmoid Curve
Characteristics
• S-shaped curve
• Flexible: can be fairly linear or approach step function
• Y = 1 / (1 + e-a(b-x-c))
100.0%
80.0%
60.0%
40.0%
20.0%
a=0.25 b=30 c=20
a=0.25 b=30 c=15
a=0.50 b=30 c=15
a=0.15 b=60 c=30
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0.0%
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Clustering
• Contiguous v. Non-Contiguous
• Absolute Dollar Difference
• Absolute Percentage Difference
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Other Clustering Ideas
• Group areas using contiguous constraints to broadly define a
territory
• Group areas within a territory without contiguity constraints to
refine territorial rating
• Consider treatment of catastrophe data
• Use of loss ratio data with premium at a common level to
reflect only differences due to territory
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Stability
Predictive stability
• Choice of perils included in data
• Number of years of data
Rating stability
• Limit movement between zones
• Use of capping
• Use of confidence intervals to help analyze changes
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Predictive Power & Stability
Predictive Power – Test #1
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1993/1994 v. 1995/1996
Correlation Coefficient
Current = New Contiguous
Non-Contiguous Better
Predictive Power – Test #2
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1993/1995 v. 1994/1996
Tested Boundaries Based on 1994/1996
Within Variance Only Marginally Better for 1994/1996 Data
Stability
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1993/1995 Clusters v. 1994/1996 Clusters
Compared Indicated Boundaries and Relativities
Little Dislocation
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