Reinsurance Property Per Risk: Constructing Size of Loss Distributions | Glenn Meyers Insurance Services Office

1. Casualty Actuaries in ReinsuranceProperty Per Risk Reinsurance Glenn Meyers Insurance Services Office, Inc. June 2-3, 2003

2. ISO’s PSOLD Product • Underlying data – Commercial property claims reported to ISO during 1991-2000 • Separate mixed exponential curves fit by: • Amount of insurance groups • Occupancy group • Subline • Coverage (Building, Contents, Building + Contents, All Causes of Loss) • Previously discussed 2000 CARe meeting http://www.casact.org/coneduc/reinsure/2000/handouts/meyers1.ppt • Will not repeat the entire presentation here • Talk about demographic features

3. Sample Input for AOI Ranges

4. Sample Input for State and Occupancy

5. The Mixed Exponential Size of Loss Distribution • i’s vary by subline and coverage • wi’s vary by AOI and occupancy group in addition to subline and coverage

6. The Mixed Exponential Size of Loss Distribution • i = mean of the ith exponential distribution • For higher i’s, a higher severity class will tend to have higher wi’s.

7. The Classification Data Availability Problem • Focus on Reinsurance Treaties • Primary insurers report data in bulk to reinsurers • Property values in building size ranges • Some classification, state and deductible information • Reinsurers can use ISO demographic information to estimate effect of unreported data.

8. Thought Experiment • Consider a database with • Amount of Insurance - AOI • State • Occupancy Group • Loss Amount • Select records that satisfy criteria – e.g. • AOI between X and Y • State = Tennessee • Apartments • Construct empirical size of loss distribution • Credibility problems

9. Database Behind PSOLD 120,000+ records (for each coverage/line combination) containing: • Severity model parameters • Amount of insurance group • 60 AOI groups • Occupancy class group • State • Number of claims applicable to the record

10. Constructing a Size of Loss Distribution Consistent with Available Data Using ISO Demographic Data • Select relevant data • Selection criteria can include: • Occupancy Class Group(s) • Amount of Insurance Range(s) • State(s) • Supply premium for each selection • Each state has different AOI and occupancy/class demographics

11. Constructing a Size of Loss Distribution for a “Selection” • Record output - Layer Average Severity • Combine all records in selection: • LASSelection = Wt Average(LASRecords) • Use the record’s claim count as weights

12. Constructing a Size of Loss Distribution for a “Selection” Where: i = ith overall weight parameter wij= ith weight parameter for the jth record Cj= Claim weight for the jth record

13. Case 1 – Very Limited Information • All occupancy classes • All amounts of insurance • All states Case 2 – State Information • All occupancy classes • All amounts of insurance • Tennessee only

14. Differences due to state demographics by occupancy and AOI

15. The Combined Size of LossDistribution for Several “Selections” • Claim Weights for a “selection” are proportional to Premium Claim Severity • LASCombined = Wt Average(LASSelection) • Using the “selection” total claim weights • The definition of a “selection” is flexible

16. The Combined Size of LossDistribution for Several “Selections” • Calculate i’s for groups for which you have pure premium information. • Calculate the average severity for jth group

17. The Combined Size of LossDistribution for Several “Selections” • Calculate the group claim weights • Calculate the weights for the treaty size of loss distribution

18. Case 1 – Very Limited Information • All occupancy classes • All amounts of insurance • All states Case 3 – AOI Information • All occupancy classes • Different AOI Groups • 50% under $250K • 30% between $250K and $500K • 20% over $500K • All States

19. Differences due to more specific AOI information

20. Sample Input for AOI Ranges Put in a lot of selections PSOLD demographics fill in within the selections

21. Sample Input for State and Occupancy Can specify state and class within each selection

22. The Deductible Problem • Most property insurance is sold with a deductible • A lot of different deductibles • PSOLD has ground up size of loss distribution as well as size of loss distributions net of deductibles

23. Size of Loss Distributions Net of Deductibles • Combine over all deductibles LASCombined Post Deductible Equals Wt Average(LASSpecific Deductible) • Weights are the number of claims over each deductible.

24. Size of Loss Distributions Net of Deductibles For an exponential distribution: Net severity Need only adjust frequency -- i.e. wi’s

25. Adjusting the wi’s • Djjth deductible amount • ij • Wi = Weighted Average gij’s

26. Case 4 = Case 1 Ground Up

27. Summary • PSOLD allows you to use whatever information you do have • Amount of insurance (limits profile) • Occupancy class group • State • Deductible • PSOLD demographic information provides a default to use when you do not get information on reinsurance treaties.

28. A Major Departure from Traditional Property Size of Loss Tabulations • Tabulate by dollars of insured value • Traditionally, property size of loss distributions have been tabulated by % of insured value.

29. Fitted $ Average Severity against Insured Value

30. Fitted Average Severity as % of Insured Value Blow up this area

31. Fitted Average Severity as % of Insured Value Eventually, assuming that loss distributions based on a percentage of AOI will produce layer costs that are too high.