1. 1 Introduction to Reinsurance Exposure Rating CAS Ratemaking Seminar Session REI-47 March 12, 2001 - Las Vegas Ira Kaplan ikaplan@gcr.com

2. 2 Exposure Rating Objectives: Estimate Expected Excess Losses n Analyze the premium profile n Estimate the expected loss ratio n Estimate the layering of the expected losses 2

3. 3 Treaty Submission: Information Needed n Premiums by policy limits What business exposes the layer to loss? n Premiums by G.L. class code How does the business expose the layer to loss? n Historic loss ratios This takes us from premiums to losses 3

4. 4 Exposure Rating Assumptions: Policy Limits Profiles n Premium Distribution by Policy Limit: Limit Est. ‘01 Premium % of Total 100/100$7,000,00017.5% 300/300 8,520,00021.3 500/50010,000,00025.0 1000/100014,480,00036.2 $40,000,000 4

5. 5 Exposure Rating Assumptions: GL class profiles n 100% Premises/Operations n 100% Table 2 5

6. 6 Distribution of Premium to Layer n Premium Distribution by Policy Limit: LimitPremiumRetention100 Xs100 Xs 200 100/1007,0007,0000 0 300/3008,5206,8421,066 612 500/50010,0007,3791,1501,471 1000/100014,4809,6411,5023,336 40,00030,8623,7175,420 n NOTE: All values in thousands 6

7. 7 The distribution of losses to layer is not the same as the distribution of premiums to layer - alae - risk load 7

8. 8 Distribution of Premium and Expected Loss to Layer: Policy Limit $500/$500 Premium Loss LayerDistributionDistribution 0-10073.8%67.8% 100-20011.5%14.7% Above 20014.7%17.5% 8

9. 9 Selection of Direct ELR n Review historic experience n Test reserve adequacy n Understand business plan changes n Review rate level changes n Selection: 40% (excl. alae) 9

10. 10 Allocation of Premium & Loss to Layer LimitRetention100 Xs100Xs200Total 100/100 Premium 7,000007,000 Loss2,800002,800 300/300 Premium6,8421,0656128,520 Loss2,5515523043,408 500/500 Premium7,3791,1501,47210,000 Loss2,7145886984,000 1000/1000 Premium9,6411,5023,33614,480 Loss3,5377661,4855,792 Total Premium30,8623,7175,42140,000 Loss11,6021,9072,49016,000 10

11. 11 ALAE and combination losses need to be included 11

12. 12 ALAE by Layer Retention100 Xs100Xs200Total Premium30,8623,7175,42140,000 ExpLoss11,6031,9072,49016,000 ALAE% 42.9% 20.9% 18.6%36.6% ALAE4,988 398 4655,851 Loss&ALAE16,5912,3042,95621,851 L&LAE Ratio53.8% 62.0% 54.5% 54.6% 12

13. 13 Loss Ratios by Layer 13

14. 14 Expected Frequency & Severity for $100,000 Layer Expected Loss$1,906,650 Expected Avg Severity$ 68,207 Expected # of Claims 27.95 14

15. 15 How to Test the Exposure Rating Indications n Review the premium profile selections n Review the selected ELR n Consider the appropriateness of the ISO loss curves n Look at actual loss information Experience Rating 15

16. 16 Pro Rata ALAE LossALAEL & ALAE Total640320960 600 x 400240120360 Ceded Loss x Direct Expenses + Ceded Loss Direct Loss = Ceded Loss x (Direct Expense + Direct Loss) Direct Loss = Ceded Loss x ( 1 + Direct Expense ) Direct Loss 16

17. 17 ALAE Treatment - case 1

18. 18 ALAE Treatment - case 2

19. 19 ALAE Load Can Vary n By layer - as seen earlier n Model with two way variability Load % decreases by limit ALAE is then allocated to layers –One allocation formula for Pro Rata –A more complicated one for Added To

20. 20 Introduction to Reinsurance Exposure Rating? NOT! n Intro to Excess of Loss Reinsurance Exposure Rating approach to estimating Loss&ALAE for GL n “Basics of Reinsurance Pricing” by David R. Clark, Exam 6 Study Note

21. 21 “Basics of Reinsurance Pricing” n Proportional Treaties n Property Per Risk XS n Casualty Per Occurrence XS WC, Umbrella, AADs n Aggregate Distributions n Property Cat n Final Price - risk loads, expenses, etc.