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Solving the Puzzle:
Reconciliation of Exposure and
Experience Rating
Stephen Philbrick
Seminar on Ratemaking
March 7-9, 2007
An Analogy
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DFA Modeling of loss ratios
Goal – develop a model of company loss ratios over
time
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Stephen Philbrick
Seminar on Ratemaking
March 7-9, 2007
Slide 2
Approach – model each line of business and combine
DFA Modeling of loss ratios
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Assume company has five lines of business (LOB)
– L1 – Commercial Property
– L2 – Homeowners
– L3 – Commercial Auto
– L4 – Med Mal
– L5 – WC
Stephen Philbrick
Seminar on Ratemaking
March 7-9, 2007
Slide 3
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Very Naïve approach – Model Li independently and
add - express Li as function of time and prior values
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Naïve approach – incorporate r(Li , Lj )
First order improvement
Stephen Philbrick
Seminar on Ratemaking
March 7-9, 2007
Slide 4
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Recognize that unanticipated trend affects all LOB
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Express Li as function of time, prior values, common
inflation model, and specific line inflation increment.
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You still need to add a dependency structure,
whether a simple correlation or a copula, but it is
limited to the causes not explained by explicit model
Second order improvement
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Recognize common drivers
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Court system
– Med mal, Comm Auto liability, Homeowners
liability
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Building material costs
– Homeowners property, Comm Property
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Stephen Philbrick
Seminar on Ratemaking
March 7-9, 2007
Slide 5
Think of this as the Masterson approach
Third order improvement
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GDP modeling
– WC claim filing propensity
– Commercial Auto exposures
– Home values
Stephen Philbrick
Seminar on Ratemaking
March 7-9, 2007
Slide 6
General Approach
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Model Li as function of
– time
– position in insurance cycle
– common inflation model
– all other exogenous variables
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Then incorporate
– correlation coefficient or copula for residuals
– error term (ei)
Stephen Philbrick
Seminar on Ratemaking
March 7-9, 2007
Slide 7
How is this applicable to Hybrid
method?
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Naïve approach
– Estimate Exposure Rate - X
– Estimate Experience Rate – Y
– Combine as w(X)+(1-w)Y
Stephen Philbrick
Seminar on Ratemaking
March 7-9, 2007
Slide 8
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It may be tempting to think the next step is to refine
the estimate of w
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Not easy, but luckily, not the right next step
Better Approach
Stephen Philbrick
Seminar on Ratemaking
March 7-9, 2007
Slide 9
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As in the DFA approach, look for common drivers
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Use the experience results of the layer, and adjacent
layers to examine the exposure rating assumptions
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Use the exposure rating assumptions to help
distinguish noise from signal in the experience rating
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Use claim count to emphasize signal over noise –
exposure model can help provide expected
frequencies
Better Approach continued
Stephen Philbrick
Seminar on Ratemaking
March 7-9, 2007
Slide 10
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Apply forensic actuarial techniques to bring the
exposure and experience models closer together
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Apply the hybrid method to the adjusted exposure
and experience models to arrive at the hybrid answer
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Optionally, weight the answer with the exposure
indication. Ideally, the indications are now much
closer, so the exact value of the weight is less
important.
Summary
Stephen Philbrick
Seminar on Ratemaking
March 7-9, 2007
Slide 11
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Both weighting of alternative methods, and use of
correlation coefficients in a model should be viewed
as the actuarial equivalent of crying “uncle”.
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Do not view weighting as a positive approach to
coming up with an answer, but a concession that
there are things going on you haven’t modeled
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Perfectly acceptable if the only remaining differences
are noise – if not, improve the model