1. Solving the Puzzle: Reconciliation of Exposure and Experience Rating Stephen Philbrick Seminar on Ratemaking 17-18 March, 2008

2. Slide 2 An Analogy DFA Modeling of loss ratios Goal – develop a model of company loss ratios over time Approach – model each line of business and combine Stephen Philbrick Seminar on Ratemaking 17-18 March, 2008

3. Slide 3 DFA Modeling of loss ratios Assume company has five lines of business (LOB) – L 1 – Commercial Property – L 2 – Homeowners – L 3 – Commercial Auto – L 4 – Med Mal – L 5 – WC Very Naïve approach – Model L i independently and add - express L i as function of time and prior values Naïve approach – incorporate  (L i, L j ) Stephen Philbrick Seminar on Ratemaking 17-18 March, 2008

4. Slide 4 First order improvement Recognize that unanticipated trend affects all LOB Express L i as function of time, prior values, common inflation model, and specific line inflation increment. 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 Stephen Philbrick Seminar on Ratemaking 17-18 March, 2008

5. Slide 5 Second order improvement Recognize common drivers Court system – Med mal, Comm Auto liability, Homeowners liability Building material costs – Homeowners property, Comm Property Think of this as the Masterson approach Stephen Philbrick Seminar on Ratemaking 17-18 March, 2008

6. Slide 6 Third order improvement GDP modeling – WC claim filing propensity – Commercial Auto exposures – Home values Stephen Philbrick Seminar on Ratemaking 17-18 March, 2008

7. Slide 7 General Approach Model L i as function of – time – position in insurance cycle – common inflation model – all other exogenous variables Then incorporate – correlation coefficient or copula for residuals – error term (e i ) Stephen Philbrick Seminar on Ratemaking 17-18 March, 2008

8. Slide 8 How is this applicable to Hybrid method? Naïve approach – Estimate Exposure Rate - X – Estimate Experience Rate – Y – Combine as w(X)+(1-w)Y It may be tempting to think the next step is to refine the estimate of w Not easy, but luckily, not the right next step Stephen Philbrick Seminar on Ratemaking 17-18 March, 2008

9. Slide 9 Better Approach As in the DFA approach, look for common drivers Use the experience results of the layer, and adjacent layers to examine the exposure rating assumptions Use the exposure rating assumptions to help distinguish noise from signal in the experience rating Use claim count to emphasize signal over noise – exposure model can help provide expected frequencies Stephen Philbrick Seminar on Ratemaking 17-18 March, 2008

10. Slide 10 Better Approach continued Apply forensic actuarial techniques to bring the exposure and experience models closer together Apply the hybrid method to the adjusted exposure and experience models to arrive at the hybrid answer 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. Stephen Philbrick Seminar on Ratemaking 17-18 March, 2008

11. Slide 11 Summary Both weighting of alternative methods, and use of correlation coefficients in a model should be viewed as the actuarial equivalent of crying “uncle”. 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 Perfectly acceptable if the only remaining differences are noise – if not, improve the model Stephen Philbrick Seminar on Ratemaking 17-18 March, 2008