INTRODUCTION TO REINSURANCE EXPERIENCE & EXPOSURE RATING UNDERWRITING INFORMATION MICHAEL E. ANGELINA - TOWERS PERRIN ROBIN MURRAY – TOWERS PERRIN CAS RATEMAKING SEMINAR MARCH 11, 2004 PHILADELPHIA, PA

AGENDA Introduction  Description of Sessions  Background Information Exposure Rating  Direct vs Ceded Loss Ratio  Treatment of ALAE Experience Rating  Burning Cost  Frequency / Severity Recap  Audience Underwriting  Reconciliation of Estimates  Concluding Remarks

BACKGROUND INFORMATION Placement Terms for Subject Business  Layer: 100K xs 100K  Loss Occurring Policy;Effective  Subject Premium $40 million  was $10 million - 6 years ago Other Information - Quantitative  Historical on-level earned premium for company  Limits distribution/line of business profile  Classes of risk (mostly Table 2 Prem/Ops)  Schedule P - loss ratios, direct, ceded, net  Listing of large losses (40 > $30,000)  Histories included with large claims  Historical loss development of ground-up losses

BACKGROUND INFORMATION

Estimation Pitfalls Effect of Policy Limit Drift on Prior Experience

BACKGROUND INFORMATION

* Ultimate Loss & ALAE as reported in Schedule P

BACKGROUND INFORMATION Observations on Data Significant growth over experience period  controlled growth or take-all-comers  expansion of current relationships with known agents  introduced new producers Appearance of underlying policy limit drift  less than 50% of business had policy limits 500k and above  2003 percentage is 64%  anticipated 2002 to 2003 saw more migration to higher limits Strong u/w results for other liability lines of business  35% to 40% on direct business  38% to 43% on net business Signs of development at later maturities  age-to-age factor of 2.78 for month

BACKGROUND INFORMATION Other Information - Qualitative  Underwriting audits  Excess and surplus company  large writer of retail supermarkets in Northeast  Underwriting philosophy generally strong  Surcharge tougher risks  Generally knowledgeable about territories  Loss ratios have been stable by accident year  Claims audit  Reserving philosophy - development on large claims across all maturities  Settlement philosophy  Higher-than-average expenses

Introduction to Exposure Rating Why Exposure Rate?  determines benchmark  incorporates changes in underlying risks  reflects distribution of policy limits  distinguishes risk profiles/classes  provides estimate where losses are sparse  eliminates issue of free cover  reflects underlying loss experience  somewhat; may not reflect excess experience  illustrates frequency and severity components  exposure curves produce average severity  implies certain frequency

Exposure Rating Methodology Distribute total premium to corresponding policy limits and lines of business  provided with premium distribution  allocation of premium to future year is critical assumption Calculate amount of premium exposed to reinsurance layer  excess loss factor / increased limits factor  reflects line of business and underlying policy limit Convert “exposed premium” to “exposed losses”  by line of business Consider other factors  ALAE; Risk Loads; ECO/XPL

Distribution of Premium to Layer Premium Distribution by Policy Limit: LimitPremiumRetention100 Xs100 Xs /1007,0007, /3008,5206,8421, /50010,0007,3791,1501, /100014,4809,6411,5023,336 40,00030,8623,7175,420 NOTE: All values in thousands

Distribution of Premium and Expected Loss to Layer: Policy Limit $500/$500 Premium Loss LayerDistribution Distribution %67.8% %14.7% Above %17.5%

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

ALAE by Layer Retention100 Xs100Xs200Total Premium30,8623,7175,42140,000 Exp Loss11,6031,9072,49016,000 ALAE% 42.9% 20.9% 18.6%36.6% ALAE4, ,851 Loss&ALAE16,5912,3042,95621,851 L&LAE Ratio53.8% 62.0% 54.5% 54.6%

ALAE Load Can Vary By layer 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