1. 1 Math 479 Casualty Actuarial Mathematics Fall 2014 University of Illinois at Urbana-Champaign Professor Rick Gorvett Session 7: Ratemaking I September 16, 2014

2. 2 Agenda Ratemaking I –Overall concept –Two basic techniques Pure premium method Loss ratio method

3. 3 Ratemaking: The Overall Concept

4. 4 Ratemaking Framework Ratemaking is an exercise in “ what-if ” –“ What if an insurer wrote a book of policies similar to that which it wrote in the past? ” –“ What if historical losses (or very similar ones) were to re-occur in the prospective policy period? How much would they cost the insurer? ” –“ What if historical policies were re-written at current rates? What would be the premium?

5. 5 Ratemaking Framework (cont.) Is this “ what-if ” tenable? Must address inherent differences between anticipated future versus past –Different types of policyholders / underwriting –Different economic / financial environment –Different judicial / legal atmosphere –Different possible outcomes from stochastic processes –Etc, etc.

6. 6 Ratemaking Framework (cont.) Premium = Losses + Expenses + Load for Profit & Contingencies

7. 7 Ratemaking: Two Basic Techniques

8. 8 (1) Pure Premium Method Project future losses per unit of exposure This is the “ pure premium ” (PP) Calculate rate per unit of exposure Rate = (PP + FE) ÷ (1 – VE – Profit) FE = fixed expenses ($)VE = variable expenses(%) Profit = profit and contingencies load (%)

9. 9 (2) Loss Ratio Method Bring historical premiums to an on-level (current) basis Adjust historical losses for –Loss development: estimate what the insurer will ultimately pay out on losses from historical periods –Loss trend: adjust losses to reflect changes in claims costs over time Frequency (per unit of exposure) changes Severity (per loss) changes

10. 10 (2) Loss Ratio Method (cont.) Relate the trended and developed historical losses to the on-level premium –Knowing expense and profit loads, this comparison will indicate whether or not, and to what degree, current rates need to be changed Adjust this indicated rate change, if necessary, for credibility considerations Take the above indicated overall rate change and spread it to multiple risk classifications and / or territories, if necessary

11. 11 (2) Loss Ratio Method (cont.) Indicated rate change = {ALR / ELR} – 1 ALR = actual loss ratio = (trended and developed losses) / (on-level premium) ELR = expected loss ratio

12. 12 Issues Data types and organization –Losses – paid, incurred,… –Premiums – written vs earned, gross vs net –AY vs PY vs CY Loss development Loss trend On-level premium –Parallelogram method Classifications

13. 13 Next Time Ratemaking II –Trend vs development – is there overlap? –Basic vs total limits losses –Parallelogram method