1. Kevin M. Madigan MHL/Paratus CAS Casualty Loss Reserve Seminar September 11, 2001 Reserving for Asbestos Pure IBNR

2. Reserving for Asbestos Pure IBNR High Excess (Re)Insurers: May have significant Asbestos pure IBNR exposure Have significant policy data issues  e.g., old policies/slips not in systems Lack valuable qualitative information

3. How to Deal With These Issues? Reserving for Asbestos Pure IBNR Research known asbestos defendants Match against policy database  May take significant effort to build DB Use historical experience to project IBNR

4. Using Experience to Project Pure IBNR Reserving for Asbestos Pure IBNR  [1] Cross, Susan L. and Doucette, John P., “Measurement of Asbestos Bodily Injury Liabilities”, PCAS, Vol LXXXIV, Nos. 160 and 161, pgs 187 -300  [2] Haidu, Jim, “Estimating a Reinsurer’s Liabilities for Asbestos and Environmental Losses”, 1996 CAS CLRS We have developed 2 report year methods inspired by:

5. Using Experience to Project Pure IBNR Reserving for Asbestos Pure IBNR Both methods use (report year) actual or modeled losses to arrive at a factor that is applied to exposed policy limits We are implicitly assuming the existence of modeled losses at the account or policy level We are modeling GROSS losses

6. Using Experience to Project Pure IBNR Reserving for Asbestos Pure IBNR Method 1 uses account experience Method 2 uses policy experience Should any of the historical experience be excluded?

7. Method I: Reserving for Asbestos Pure IBNR “Pricing” Approach  Allocate experience to layers  Calculate burn rates  Apply to potential IBNR policies

8. Method I: Reserving for Asbestos Pure IBNR  Allocate experience to layers  Each account has an actual (closed accounts) or modeled (open accounts) annual loss distribution

9. $500,000 $4,000,000 $5,000,000 $10,000,000 $5,000,000 $500,000 $0 $10,000,000 $6,000,000 $0 $250,000 Account: ABC Asbestos Co. Insulations R Us Acme Widgets TOTAL Annual Loss:$35,000,000$16,000,000$250,000$51,250,000 $500,000 $4,000,000 $5,000,000 $10,000,000 $20,000,000 $11,000,000 $750,000 Burn Rate 33.33% 66.67% 36.67% 50.00% Method I: Reserving for Asbestos Pure IBNR  Calculation of Burn Rates  Example for Report Year 19XX Layers $500,000$1,000,000 $5,000,000 $10,000,000 $20,000,000 $30,000,000 $40,000,000 $0$500,000

10.  Ideally want burn rate confidence intervals, from which baseline confidence intervals can be selected for each layer Burn Rate Confidence Intervals Method I: Reserving for Asbestos Pure IBNR  Calculation of Burn Rates Layer $0$500,000 $1,000,000 $5,000,000 $10,000,000 $20,000,000 $30,000,000 $40,000,000 RY 1990 45%70% 44%68% 42%64% 23%45% 15%34% 2%16% 1%10% RY 1991 46%67% 46%67% 25%52% 12%40% 1%5% 0% RY 1992 40%80% 40%80% 40%80% 35%78% 30%75% 12%46% 3%37%

11. Method I: Reserving for Asbestos Pure IBNR  Apply Burn Rates to potential IBNR policies  Requires assumptions regarding: Reporting Pattern(s) Trend Assumptions –e.g., 2% annual decay in burn rate Exposed Policy Limits

12. Method I: Lower limit of C.I. of Burn Rate for Layer: Exposure in Layer: Year% ReportedTrend FactorProjected Ultimate Losses 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 10.4% 9.4% 8.5% 7.7% 7.1% 6.4% 5.9% 5.4% 4.9% 4.5% 4.2% 3.8% 3.5% 3.3% 3.0% 2.8% 2.6% 2.4% 2.2% 2.0% 0.980 0.960 0.941 0.922 0.904 0.886 0.868 0.851 0.834 0.817 0.801 0.785 0.769 0.754 0.739 0.724 0.709 0.695 0.681 0.668 $500,000,000 Reserving for Asbestos Pure IBNR 26% TOTAL: $13,200,299 $11,717,663 $10,424,130 $9,291,765 $8,297,446 $7,421,905 $6,648,983 $5,965,055 $5,358,567 $4,819,680 $4,339,976 $3,912,226 $3,530,194 $3,188,488 $2,882,427 $2,607,937 $2,361,460 $2,139,885 $1,940,481 $1,760,847 $111,809,413  Apply Burn Rates

13. Comparison of Methods: Reserving for Asbestos Pure IBNR Method I computes an annual ‘rate’ for each layer, and ‘charges’ the exposed policies the corresponding ‘price’. Method II computes one factor to be applied to the limits of each policy

14. But wait! Reserving for Asbestos Pure IBNR We have a wide assortment of attachment points and policy limits, so it hardly seems right to apply the same factor to each policy. Does a $25M x $200M policy have the same exposure to loss as a $4M x $1M policy? Of course not!

15. Method II: Reserving for Asbestos Pure IBNR Exposed policy limits are ‘adjusted’ Adjusted exposure = TPE * Pr( GUL > AP) as follows: where:TPE=Total Policy Exposure GUL=Ground-Up Loss AP=Policy Attachment Point

16. Method II: Reserving for Asbestos Pure IBNR  Calculate historical ratios of loss to adjusted exposure for each report year (let’s call them loss cost factors)  Select a base line confidence interval for the loss cost factors  Make assumptions regarding reporting pattern(s) and cost trend(s)

17.  Calculate ratios of loss to adjusted exposure Method II: Policy Att PointPr(GUL > AP)Policy Limit Adjusted Exposure Policy Loss $1,000,000 $5,000,000 $10,000,000 $15,000,000 $20,000,000 $25,000,000 40.0% 30.0% 20.0% 10.0% 5.0% 1.0% $500,000 $1,500,000 $4,000,000 $15,000,000 $5,000,000 $25,000,000 $200,000 $600,000 $1,200,000 $3,000,000 $500,000 $250,000 $2,500 $0 $5,000,000 $0 $1,000 TOTALS:$6,000,000$5,006,000 Reserving for Asbestos Pure IBNR LOSS COST FACTOR: 0.834  Example: RY 19xx

18. Baseline Loss Cost Factor: 0.834 Year% ReportedTrend FactorProduct 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 10.4% 9.4% 8.5% 7.7% 7.1% 6.4% 5.9% 5.4% 4.9% 4.5% 4.2% 3.8% 3.5% 3.3% 3.0% 2.8% 2.6% 2.4% 2.2% 2.0% 0.980 0.960 0.941 0.922 0.904 0.886 0.868 0.851 0.834 0.817 0.801 0.785 0.769 0.754 0.739 0.724 0.709 0.695 0.681 0.668 0.102 0.090 0.080 0.071 0.064 0.057 0.051 0.046 0.041 0.037 0.033 0.030 0.027 0.025 0.022 0.020 0.018 0.016 0.015 0.014 0.860 Method II: Reserving for Asbestos Pure IBNR Trended Projected Loss Cost Factor: 0.717  Select a base line for the loss cost factors

19. Trended Projected Loss Cost Factor:0.717 Potential Policies Adjusted Exposure Projected Losses Att PointPr(GUL > AP)Limit $25,000,000 $40,000,000 $75,000,000 $125,000,000 $250,000,000 1.000% 0.800% 0.600% 0.400% 0.325% $5,000,000 $10,000,000 $25,000,000 $50,000,000 $50,000 $80,000 $150,000 $100,000 $162,500 $35,850 $57,360 $107,550 $71,700 $116,513 TOTALS:$115,000,000$542,500$388,973 Reserving for Asbestos Pure IBNR Method II:  Make assumptions regarding reporting pattern(s) and cost trend(s)

20. Other Issues: Reserving for Asbestos Pure IBNR Loss trend may be (probably is?) positive, or trend rate may not be constant Policy “buy backs” Distinguish products liability from other liability Not only source of “pure” IBNR Commutation strategy Reinsurance collections/collectibility