1 Math 479 / 568 Casualty Actuarial Mathematics Fall 2014 University of Illinois at Urbana-Champaign Professor Rick Gorvett Session 11: Individual Risk Rating October 2, 2014

2 Agenda Individual Risk Rating –Types of plans –Prospective rating –Retrospective rating

3 Approaches to Ratemaking Ratemaking: the development of rates (per unit of exposure) and premiums for entities given various characteristics, loss experiences, etc. Two broad categories: (1) Manual ratemaking Looked up in a “ rate manual ” For members of groups with similar characteristics Use historical aggregate loss statistics Possible adjustments for particular risk characteristics, loss experience

4 Approaches to Ratemaking (cont.) (2) Individual risk rating Calculated for relatively “ large ” insureds Use insured data, possibly supplemented by more general data –Credibility considerations Premium can be based upon a prospective or a retrospective system –Prospective: past loss experience  future rates –Retrospective: actual policy period experience leads to appropriate adjustments in premium after the policy period

5 Prospective Rating Schedule rating –Reflects risk characteristics of insured Does not directly reflect insured ’ s historical loss experience –Percentage debits or credits are applied to manual rates Add up percentages and apply to the manual premium (manual premium = manual rate per exposure × number of exposures) Credits lower the premium, debits increase it Subject to a maximum or minimum total modification

6 Prospective Rating (cont.) Schedule rating (cont.) –Examples of debit / credit characteristic categories (from ISO Table) Location of insured ’ s premises Condition and care of premises Condition and care of equipment Classification peculiarities Employee training, supervision, selection, experience Cooperation – medical facilities, safety program –For each type of characteristic, there is a range of possible debits and credits (e.g., up to +/- 5%)

7 Schedule Rating Example A large manufacturer purchases a commercial general liability insurance policy which is schedule-rated. The exposure base is sales. The manufacturer has annual sales of $10 million, and the manual rate is $5.25 per $1,000 of sales. The following schedule rating credits and debits apply to the manufacturer: A. Location3% credit B. Premises1% debit C. Equipment8% credit D. Classification Peculiarities7% credit E. Employees6% credit F. Cooperation2% debit The maximum schedule rating modification is 25% up or down. (1) Based on this information, what is the schedule-rated premium for this manufacturer? (2) You realize that the Premises adjustment above should not have been a 1% debit, but a 5% credit. All other adjustments are correct. Re-calculate the schedule-rated premium for this manufacturer.

8 Prospective Rating (cont.) Experience rating –Losses – adjust for exposure changes, trend, development –Exposures and premiums – bring to on-level basis –Credibility of insured ’ s data – varies from 0 to 1 –Relationship of adjusted historical losses (trended and developed to the prospective policy period) to exposures (or premiums) yields an indication of an appropriate premium level –Generally there is a specified minimum and maximum premium level

9 Retrospective Rating Actual losses (and usually ALAE) during the policy period are used to retrospectively adjust the original premium paid. “ Deposit ” premium up-front. Periodically, after end of policy period, actual losses are used as the basis for adjusting the premium. –Use a “ loss development factor ” (LDF) to bring to an estimated ultimate loss basis. Min. and max. premiums are agreed upon. Premium formula: Retrospective premium = [Basic premium + {reported losses × loss conversion factor}] × Tax multiplier

10 Retro Rating Example The following information is available with respect to a retrospectively rated insurance policy: Manual premium = $ 250,000 Experience modification factor: 5% credit Basic premium factor = 0.12 Loss conversion factor = 1.20 Minimum retro premium = $ 200,000 Maximum retro premium = $300,000 Tax multiplier = 1.03 Reported incurred losses = $ 210,000 Find the retrospective premium indicated by this information.

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