March 12, 1999 James D. Hurley Claims-Made Ratemaking Casualty Actuarial Society - Seminar on Ratemaking INT-6: Basic Techniques for Other Commercial Lines

Claims-Made Ratemaking G:\DEGRENJ\JIM\PRESENT\CASRatemaking.ppt 2 Advantages of Claims-Made Relative to Occurrence  Insured  Price is less if underlying trend is positive  Ability to keep policy limits current  Availability greater  Insurer  No IBNR - reserving and pricing easier, more accurate  With an unexpected change in trend, claims-made more correct  Shorter time horizon on future forecasts  Willing to offer claims-made where occurrence not viewed as option

Claims-Made Ratemaking G:\DEGRENJ\JIM\PRESENT\CASRatemaking.ppt 3 Disadvantages of Claims-Made Relative to Occurrence  Insured  Understanding of coverage is not as great  Report date may be manipulated  Tail coverage - cost and understanding  Large price increases going from first year to mature  Insurer  Less investment income  Unfavorable Federal income tax treatment with use of industry payment pattern  Change in limits or specialty difficult to rate correctly  Historical data may be inappropriate when switching from occurrence to claims-made

Claims-Made Ratemaking G:\DEGRENJ\JIM\PRESENT\CASRatemaking.ppt 4 Claims-made maturity has no occurrence counterpart Different dimension of loss development  Claims-made has no “true” IBNR  Development by lag (RY - AY) Exposures have 1-D in occurrence and 2-D for claims-made Tail coverage links claims-made and occurrence Rate making Differences - Claims-made vs. Occurrence

Claims-Made Ratemaking G:\DEGRENJ\JIM\PRESENT\CASRatemaking.ppt 5 Retro Date & Claims-Made Coverage MD who has coverage in 1988, began 1st year claims-made in 1985 Retroactive Date: 1/1/85 Definition: Occurrences on or after the retro date are covered by the claims-made policy.

Claims-Made Ratemaking G:\DEGRENJ\JIM\PRESENT\CASRatemaking.ppt 6 Retro Date & Claims-Made Coverage MD who has coverage in 1988, began mature claims-made in 1985 Retroactive Date: Prior to 1983

Claims-Made Ratemaking G:\DEGRENJ\JIM\PRESENT\CASRatemaking.ppt 7 Tail Coverage MD who began 1st year C-M in 1985, left at end of 1988 without tail

Claims-Made Ratemaking G:\DEGRENJ\JIM\PRESENT\CASRatemaking.ppt 8 Tail Coverage MD who began 1st year C-M in 1985, purchased tail at end of 1988

Claims-Made Ratemaking G:\DEGRENJ\JIM\PRESENT\CASRatemaking.ppt 9 Data & Lags

Claims-Made Ratemaking G:\DEGRENJ\JIM\PRESENT\CASRatemaking.ppt 10 Data & Lags Note: Lag = Report Year - Accident Year

Claims-Made Ratemaking G:\DEGRENJ\JIM\PRESENT\CASRatemaking.ppt 11 Data & Lags

Claims-Made Ratemaking G:\DEGRENJ\JIM\PRESENT\CASRatemaking.ppt 12 Ratemaking Data Sum of Latest Diagonal = 655

Claims-Made Ratemaking G:\DEGRENJ\JIM\PRESENT\CASRatemaking.ppt 13 Ratemaking Data Sum of Latest Diagonal = 655

Claims-Made Ratemaking G:\DEGRENJ\JIM\PRESENT\CASRatemaking.ppt 14 Ratemaking Data

Claims-Made Ratemaking G:\DEGRENJ\JIM\PRESENT\CASRatemaking.ppt 15 Exposure based approach necessary Why?  Handle various maturities/classes  Identify difference between development/emergence  L/R methods distorted by changes in reporting patterns Require 2-D grid  No occurrence equivalent  Handle C-M entry (1st, 2nd, etc.)  Handle exit (tail vs. no tail)  Handle change in classes Ratemaking Data Exposures -

Claims-Made Ratemaking G:\DEGRENJ\JIM\PRESENT\CASRatemaking.ppt 16 Ratemaking Data Exposure

Claims-Made Ratemaking G:\DEGRENJ\JIM\PRESENT\CASRatemaking.ppt 17 Ratemaking Data Exposure - Class 1 Basis

Claims-Made Ratemaking G:\DEGRENJ\JIM\PRESENT\CASRatemaking.ppt 18 Require AY by RY Why?  Loss corollary to 2-D exposure  Support development/emergence pattern distinction  AY only; lose RY consideration  RY only; lose exposure distinction and development can vary by lag Procedure  A data triangle represents current evaluation  Calculate LDF’s by lag and age since report  Apply by cell to derive ultimate Ratemaking Data Losses

Claims-Made Ratemaking G:\DEGRENJ\JIM\PRESENT\CASRatemaking.ppt 19 Data & Method - The 3rd Dimension Valued at 12/31/88

Claims-Made Ratemaking G:\DEGRENJ\JIM\PRESENT\CASRatemaking.ppt 20 Method - Simplified Development by Lag

Claims-Made Ratemaking G:\DEGRENJ\JIM\PRESENT\CASRatemaking.ppt 21 Method - Development by Lag * Assumed same as Lag 2.

Claims-Made Ratemaking G:\DEGRENJ\JIM\PRESENT\CASRatemaking.ppt 22 Method - Developed Reported Developed to Ultimate

Claims-Made Ratemaking G:\DEGRENJ\JIM\PRESENT\CASRatemaking.ppt 23 Calculate pure premium (or frequency/severity) in AY RY detail Analysis of trends; reporting patterns Expenses - consider flat loading Recognize ILF differences Method Next Steps -