1. 1 Math 479 / 568 Casualty Actuarial Mathematics Fall 2014 University of Illinois at Urbana-Champaign Professor Rick Gorvett Session 9: Risk Classification September 30, 2014

2. 2 Agenda Ratemaking “ relativities ” Risk classification

3. 3 Ratemaking “ Relativities ” Three kinds of relativities –Classification –Territorial –Increased limits Classification ratemaking –One class serves as the “ base class ” (relativity = 1.00) –Rates for other classes are keyed off of the base class rate Class rate = base rate × class relativity factor

4. 4 Ratemaking “ Relativities ” (cont.) Classification ratemaking (cont.) –Ratemaking process 1)Determine indicated overall rate change 2)Determine on-level premium for each class 3)Convert on-level EP by class to a base-class-equivalent by dividing by the existing class relativities 4)Determine loss ratio for each class, using base-class- equivalent on-level EP 5)Determine indicated class relativities by dividing each class ’ s loss ratio by the base class loss ratio 6)Use an off-balance factor to determine the base rate necessary to achieve the overall indicated rate change 7)If necessary, limit rate changes by class to any existing regulatory restrictions, and adjust to yield the overall indicated rate change

5. 5 Ratemaking “ Relativities ” (cont.) Territorial ratemaking –Very similar to classification ratemaking, conceptually and procedurally Increased limits factors –Basic limits premium or loss cost E.g., $100,000 per occurrence limit –Calculate premiums or loss costs for higher policy limits by multiplying the basic limits value by the appropriate increased limits factor (ILF)

6. 6 Risk Classification Differential premiums –Group characteristics determine the class –Different characteristics imply different underlying loss propensities, and thus different indicated / required premiums Costs that may vary by group: –Losses –Risk – variation from expected values; e.g., more heterogeneity within a group implies more potential adverse selection –Expenses –Investment income – e.g., long- versus short-tailed LoBs

7. 7 Risk Classification Rating Variables Criteria for selecting rating variables –Statistical or actuarial Accuracy and fairness Homogeneity Credibility Reliability or predictive stability –Operational or practical Objectively defined Administrative expense Verifiability

8. 8 Rating Variables (cont.) Criteria for selecting rating variables (cont.) –Social Socially acceptable Privacy issues Causality – intuitively understandable underlying economic or risk management link of rating variable to insurance cost Controllability Affordability –Legal State regulations Federal equal protection clause

9. 9 2006 CAS Exam 5, #39

10. 10 2004 CAS Exam 5, #36