march 12, 1999 james d. hurley claims-made ratemaking casualty actuarial society - seminar on...

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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G:\DEGRENJ\JIM\PRESENT\CASRatemaking.ppt

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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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 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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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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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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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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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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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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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

6

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Data & Lags

Note: Lag = Report Year - Accident Year

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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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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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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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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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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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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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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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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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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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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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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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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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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 -

march 12, 1999 james d. hurley claims-made ratemaking casualty actuarial society - seminar on...

Documents

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