Math 479 / 568 Casualty Actuarial Mathematics

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. Agenda • Ratemaking “relativities” • Risk classification

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

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. 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. 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. 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. 2006 CAS Exam 5, #39

10. 2004 CAS Exam 5, #36