March 12, 1999
James D. Hurley
Claims-Made Ratemaking
Casualty Actuarial Society - Seminar on Ratemaking
INT-6: Basic Techniques for Other Commercial Lines
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Claims-Made Ratemaking
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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
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Claims-Made Ratemaking
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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
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Claims-Made Ratemaking
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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
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Claims-Made Ratemaking
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Report (Coverage) YearAccident
Year 1985 1986 1987 1988 1989 1990 >1990
1985 X X X X1986 X X X1987 X X1988 X
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.
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Claims-Made Ratemaking
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Report (Coverage) YearAccident
Year 1985 1986 1987 1988 1989 1990 >1990
Prior X X X1983 X X1984 X
1985 X X X X1986 X X X1987 X X1988 X
Retro Date & Claims-Made Coverage
MD who has coverage in 1988, began mature claims-made in 1985
Retroactive Date: Prior to 1983
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Claims-Made Ratemaking
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Report (Coverage) YearAccident
Year 1985 1986 1987 1988 1989 1990
1985 X X X X
1986 X X X
1987 X X
1988 X
Tail Coverage
MD who began 1st year C-M in 1985, left at end of 1988 without tail
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Claims-Made Ratemaking
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Report (Coverage) YearAccident
Year 1985 1986 1987 1988 1989 >1989
1985 X X X X X X
1986 X X X X X
1987 X X X X
1988 X X X
Tail Coverage
MD who began 1st year C-M in 1985, purchased tail at end of 1988
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Claims-Made Ratemaking
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Report YearAccident
Year 1984 1985 1986 1987 1988 1989
1984 840 841 842 843 844 845
1985 850 851 852 853 854
1986 860 861 862 863
1987 870 871 872
1988 880 881
Data & Lags
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Claims-Made Ratemaking
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Report YearLag 1
(84) 2 (85)
3 (86)
4 (87)
5 (88)
6 (Etc)
0 840 840 840 840 840 ETC
1 851 851 851 851 ETC
2 862 862 862 ETC
3 873 873 ETC
4 884 ETC
5 ETC
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Data & Lags
Note: Lag = Report Year - Accident Year
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Claims-Made Ratemaking
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ClaimNumber
Lag(RY – AY) 12 Mos. 24 Mos.
Beyond24 Mos.
1 0 100 120 120
2 1 50 60 60
3 2 10 15 15
Data & Lags
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Claims-Made Ratemaking
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AccidentYear 12 Mos. 24 Mos. 36 Mos. 48 Mos.
1985 100 170 190 195
1986 100 170 190
1987 100 170
1988 100
Ratemaking Data
Sum of Latest Diagonal = 655
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Claims-Made Ratemaking
G:\DEGRENJ\JIM\PRESENT\CASRatemaking.ppt
AccidentYear 12 Mos. 24 Mos. 36 Mos. 48 Mos.
1985 100 120 120 120
1986 150 180 180
1987 160 195
1988 160
Ratemaking Data
Sum of Latest Diagonal = 655
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Claims-Made Ratemaking
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Report YearAccident
Year 1985 1986 1987 1988AY
Totals
1985 120 60 15 0 195
1986 120 60 10 190
1987 120 50 170
1988 100 100
RY Totals 120 180 195 160 655
Ratemaking Data
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Claims-Made Ratemaking
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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 -
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Claims-Made Ratemaking
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MDCoverageEffective
RetroDate
ExpirationDate Tail Class
Class 1Basis
1 1/1/85 1/1/85 12/31/85 Y 1 1.0
2 1/1/85 1/1/85 12/31/87 N 3 3.0
3 1/1/85 1/1/85 N/A N/A 5 5.0
Ratemaking Data
Exposure
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Claims-Made Ratemaking
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Report Year
AccidentYear 1985 1986 1987 1988
1985 9.0 9.0 9.0 6.0
1986 8.0 8.0 5.0
1987 8.0 5.0
1988 5.0
Ratemaking Data
Exposure - Class 1 Basis
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Claims-Made Ratemaking
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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 DataLosses
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Claims-Made Ratemaking
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Report YearAccident
Year 1985 1986 1987 1988AY
Totals
1985 120 60 15 0 195
1986 120 60 10 190
1987 120 50 170
1988 100 100
RY Totals 120 180 195 160 655
Data & Method - The 3rd Dimension
Valued at 12/31/88
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Claims-Made Ratemaking
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Case Development
RY = AY 100 120 120 120
RY = AY + 1 50 60 60
RY = AY + 2 10 15
Total 100 170 190 195
12 24 36+
Lag 0 1.20 1.00 1.00
Lag 1 1.20 1.00 N/A
Lag 2 1.50 N/A N/A
Method - Simplified Development by Lag
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Claims-Made Ratemaking
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Report Year
AccidentYear 1985 1986 1987 1988
1985 1.00 1.00 1.00 1.50*
1986 1.00 1.00 1.50
1987 1.00 1.20
1988 1.20
Method - Development by Lag
* Assumed same as Lag 2.
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Claims-Made Ratemaking
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Report YearAccident
Year 1985 1986 1987 1988AY
Totals
1985 120 60 15 0 195
1986 120 60 15 195
1987 120 60 180
1988 120 120
RY Totals 120 180 195 195 690
Method - Developed Reported
Developed to Ultimate
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Claims-Made Ratemaking
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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 -