1. Many rating variables are correlated.
2. Using a multivariate approach removes potential double-counting and can account for interaction effects.
BAILEY'S MINIMUM BIAS
1.First scenario. To guess factor for one variable (from pure premium).
Class
|
Pure Premium
|
Relativity
|
Age group 1
|
$450
|
1
|
Age group 2
|
$1570
|
3.5
|
The exposure and rating plan is given as follow.
Exposures
|
Pure Premium
|
|||||
Car Size
|
Car Size
|
|||||
Large
|
Medium
|
Small
|
Large
|
Medium
|
Small
|
|
1
|
100
|
1,200
|
500
|
10,000
|
120,000
|
50,000
|
2
|
300
|
500
|
400
|
105,000
|
175,000
|
140,000
|
Calculate the Loss Ratio Relativity
Car size
|
Theoretical Premium
|
Theoretical Loss Ratio
|
Loss Ratio Relativity
|
Large
|
115,000
|
1.30
|
1.00
|
Medium
|
295,000
|
3.70
|
2.80
|
Small
|
190,000
|
7.50
|
5.70
|
2. Second Scenario. Same exposure but different rating plan.
Exposures
|
Pure Premium
|
|||||
Car Size
|
Car Size
|
|||||
Large
|
Medium
|
Small
|
Large
|
Medium
|
Small
|
|
1
|
100
|
1,200
|
500
|
10,000
|
336,000
|
285,000
|
2
|
300
|
500
|
400
|
30,000
|
140,000
|
228,000
|
Calculate the Loss Ratio Relativity (Instead of pure premium, Use loss ratio)
Age group
|
Theoretical Premium
|
Theoretical Loss Ratio
|
Loss Ratio Relativity
|
Age group 1
|
631,000
|
1.3
|
1
|
Age group 2
|
398,000
|
4.7
|
3.7
|
3. To continue interating
Class
|
Scenario 1
|
Scenario
2
|
Scenario
3
|
Scenario
4
|
Scenario
5
|
Scenario
6
|
Large Car
|
1
|
1
|
1
|
1
|
1
|
1
|
Medium Car
|
2.8
|
2.8
|
2.9
|
2.9
|
2.9
|
2.9
|
Small Car
|
5.7
|
5.7
|
5.8
|
5.8
|
5.8
|
5.8
|
Age Group 1
|
1
|
1
|
1
|
1
|
1
|
1
|
Age Group 2
|
3.5
|
3.7
|
3.7
|
3.6
|
3.6
|
3.6
|
4. This example assumed two multiplicative factors (age and vehicle type), but approach can be modified for more variables and/or additive rating plans.
GENERALIZED LINEAR MODELS
1. Generalized Linear Models (GLM) is a generalized framework for fitting multivariate linear models. Bailey's method is an example.
CURVE FITTING
1. Can calculate certain type of relativities using smooth curves. Fit exposure data to a curve.
2. Assume the distribution of exposures by amount of insurance is log normal.
3. Assume the cumulative loss distribution has a functional relationship to the cumulative exposure distribution
4. (losses at A / total losses) / (exposures at A / total exposures) = pure premium at A/ total pure premium
