Solving the Puzzle: Reconciliation of Exposure and Experience Rating

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

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. DFA Modeling of loss ratios • Assume company has five lines of business (LOB) • L1 – Commercial Property • L2 – Homeowners • L3 – Commercial Auto • L4 – Med Mal • L5 – WC • Very Naïve approach – Model Li independently and add - express Li as function of time and prior values • Naïve approach – incorporate r(Li , Lj ) Stephen Philbrick Seminar on Ratemaking 17-18 March, 2008

4. First order improvement • Recognize that unanticipated trend affects all LOB • Express Li 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. 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. Third order improvement • GDP modeling • WC claim filing propensity • Commercial Auto exposures • Home values Stephen Philbrick Seminar on Ratemaking 17-18 March, 2008

7. General Approach • Model Li 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 (ei) Stephen Philbrick Seminar on Ratemaking 17-18 March, 2008

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. 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. 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. 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