1999 clrs intermediate case study discussion material for gl insurance company

1999 CLRSIntermediate Case Study

Discussion Material For GL Insurance Company

Intermediate Case StudyCompany Facts

• Stock insurance company• Only general liability policies written• In business for over 20 years• Stable book of business (essentially the same group of insureds)• Well managed• Healthy balance sheetGL-1

Intermediate Case Study Balance Sheet @ 12/31/98 ($000)

Bonds $463,388

Stocks $48,262

Cash $11,028

Total Invested Assets $522,678

Agents' Balance $19,799

Other Assets $35,662

Total Assets $578,139

Assets

Loss & LAE ReservesCase Reserves $208,052IBNR Reserves $198,304

Unearned Premium Reserve $84,196

Other Liabilities $24,965

Total Liabilities $515,517

Policyholders' Surplus $62,622

Total Liabilities & Surplus $578,139

Liabilities & Surplus

GL-2

Intermediate Case StudyReserving Information

• GL Insurance Company has a small actuarial staff headed by an actuarial student.

• The department calculated year-end reserves using both the paid and incurred loss development methods.

• The staff supplements this analysis with the use of expected loss techniques, if needed.

GL-3

Intermediate Case StudyGLIC Actuarial Study

Slides GL-5 and GL-6 display the paid loss development method.

Slides GL-7 and GL-8 display the incurred loss development method.

Tail factor selections are based upon reviews of industry data, as well as curve fits of selected loss development factors (Slides GL-6 and GL-8).

GL-4

Total General LiabilityPaid Loss Development Method

AccidentYear 12 24 36 48 60 72 84 96 108 120 132

1988 $1,340 $3,188 $5,072 $6,973 $8,677 $10,008 $11,802 $12,606 $13,174 $13,596 $14,0331989 1,857 4,297 6,864 9,438 11,820 13,594 14,783 15,710 16,439 16,9721990 2,024 4,891 7,790 10,773 13,792 16,071 17,695 18,886 19,7351991 2,781 6,655 10,671 14,738 18,022 20,795 23,179 24,5971992 3,439 8,272 13,325 18,551 23,386 26,861 29,4091993 3,714 9,039 14,638 20,326 26,117 30,6431994 4,652 11,236 18,109 25,239 31,2501995 5,292 12,974 21,106 29,6111996 6,818 16,984 27,6771997 9,337 23,2631998 15,073

AccidentYear 12-24 24-36 36-48 48-60 60-72 72-84 84-96 96-108 108-120 120-132 132+

1988 2.379 1.591 1.375 1.244 1.153 1.179 1.068 1.045 1.032 1.0321989 2.314 1.597 1.375 1.252 1.150 1.087 1.063 1.046 1.0321990 2.417 1.593 1.383 1.280 1.165 1.101 1.067 1.0451991 2.393 1.603 1.381 1.223 1.154 1.115 1.0611992 2.405 1.611 1.392 1.261 1.149 1.0951993 2.434 1.619 1.389 1.285 1.1731994 2.415 1.612 1.394 1.2381995 2.452 1.627 1.4031996 2.491 1.6301997 2.491

3 Avg 2.478 1.623 1.395 1.261 1.159 1.104 1.064 1.045 1.032 1.0323 Wtd Avg 2.482 1.624 1.396 1.259 1.160 1.103 1.064 1.045 1.032 1.0325 Avg 2.457 1.620 1.392 1.257 1.158 1.115 1.065 1.045 1.032 1.032Mid 3 of 5 2.459 1.619 1.391 1.260 1.156 1.104 1.065 1.045Wtd Avg 2.443 1.615 1.390 1.255 1.159 1.109 1.064 1.045 1.032 1.032

Selected 2.491 1.623 1.395 1.261 1.152 1.104 1.065 1.045 1.032 1.032

Age-to-Age Development Factors

Paid Losses ($000)

GL INSURANCE COMPANY

GL-5


Total General LiabilityAnalysis of Development Patterns-- Paid LossesUsing "The Method of Least Squares"

X Var. Y VariableAge-to-Age X' Y' X' Y'

Age Factors X ln[ln(Y)] ln (X) ln[ln(Y/(Y-1)] X Y X Y

12 2.491 12 (0.09) 2.48 (0.67) 12 2.085 12 2.49224 1.623 24 (0.73) 3.18 (0.04) 24 1.644 24 1.65236 1.395 36 (1.10) 3.58 0.23 36 1.400 36 1.36748 1.261 48 (1.46) 3.87 0.45 48 1.256 48 1.22860 1.152 60 (1.96) 4.09 0.71 60 1.167 60 1.15072 1.104 72 (2.31) 4.28 0.86 72 1.110 72 1.10284 1.065 84 (2.77) 4.43 1.03 84 1.073 84 1.07196 1.045 96 (3.12) 4.56 1.15 96 1.049 96 1.050

108 1.032 108 (3.46) 4.68 1.25 108 1.033 108 1.036120 1.032 120 (3.46) 4.79 1.25 120 1.022 120 1.026

132 1.015 132 1.019660 (20.45) 39.95 6.21 144 1.010 144 1.01466 (2.05) 4.00 0.62 156 1.007 156 1.010

168 1.005 168 1.007Parameter Estimates 180 1.003 180 1.005N= 10 10 192 1.002 192 1.004A= 2.961 0.061 204 1.001 204 1.003B= 0.968 0.857 216 1.001 216 1.002

228 1.001 228 1.002R 2̂= 0.984 0.996 240 1.000 240 1.001

252 1.000 252 1.001264 1.000 264 1.001276 1.000 276 1.001288 1.000 288 1.000

Fitted Tail Factor from 132 to Ultimate 1.047 1.072

Broader Data Source - Bests Casualty Loss Reserve Development Series 1.135

Selected Tail Factor 1.075

Weibull ModelFitted Values

A ̂(B ̂X)

Actual Values

1/ [1-EXP(-A * X ̂B)]

Power Model Weibull ModelCurve: Y = Curve: Y =

Transformed Values

AverageTotal

Power ModelFitted Values

Transformed Values

GL-6

GL Insurance Company

Total General LiabilityIncurred Loss Development Method

AccidentYear 12 24 36 48 60 72 84 96 108 120 132

1988 $5,662 $8,879 $11,006 $12,396 $13,067 $13,526 $13,838 $14,075 $14,315 $14,573 $14,7781989 6,975 10,897 13,556 15,303 16,271 16,861 17,252 17,565 17,883 18,2081990 8,345 13,012 16,304 18,417 19,507 20,224 20,677 21,077 21,4651991 10,652 17,073 21,391 23,978 25,469 26,443 27,073 27,5501992 13,647 21,807 27,086 30,684 32,600 33,807 34,5841993 15,549 24,872 31,261 35,432 37,460 38,9651994 18,260 29,200 36,605 41,696 44,4881995 22,029 35,312 44,500 50,3221996 28,730 46,297 58,0611997 39,637 64,6281998 55,297

AccidentYear 12-24 24-36 36-48 48-60 60-72 72-84 84-96 96-108 108-120 120-132 132+

1988 1.568 1.240 1.126 1.054 1.035 1.023 1.017 1.017 1.018 1.0141989 1.562 1.244 1.129 1.063 1.036 1.023 1.018 1.018 1.0181990 1.559 1.253 1.130 1.059 1.037 1.022 1.019 1.0181991 1.603 1.253 1.121 1.062 1.038 1.024 1.0181992 1.598 1.242 1.133 1.062 1.037 1.0231993 1.600 1.257 1.133 1.057 1.0401994 1.599 1.254 1.139 1.0671995 1.603 1.260 1.1311996 1.611 1.2541997 1.630

3 Avg 1.615 1.256 1.134 1.062 1.038 1.023 1.018 1.018 1.018 1.0143 Wtd 1.618 1.256 1.134 1.062 1.039 1.023 1.018 1.018 1.018 1.0145 Avg 1.609 1.253 1.131 1.062 1.038 1.023 1.018 1.018 1.018 1.014Mid 3 of 5 1.605 1.255 1.132 1.061 1.037 1.023 1.018 1.018Wtd 1.605 1.253 1.131 1.062 1.038 1.023 1.018 1.018 1.018 1.014

Selected 1.621 1.256 1.134 1.062 1.038 1.023 1.018 1.018 1.018 1.014

Incurred Losses ($000)


GL-7


Total General LiabilityAnalysis of Development Patterns-- Incurred LossesUsing "The Method of Least Squares"



12 1.621 12 (0.73) 2.48 (0.04) 12 1.306 12 1.56224 1.256 24 (1.48) 3.18 0.46 24 1.198 24 1.24436 1.134 36 (2.07) 3.58 0.76 36 1.130 36 1.13448 1.062 48 (2.81) 3.87 1.04 48 1.086 48 1.08160 1.038 60 (3.29) 4.09 1.20 60 1.058 60 1.05272 1.023 72 (3.78) 4.28 1.33 72 1.039 72 1.03484 1.018 84 (4.03) 4.43 1.40 84 1.026 84 1.02496 1.018 96 (4.03) 4.56 1.40 96 1.018 96 1.016

108 1.018 108 (4.03) 4.68 1.40 108 1.012 108 1.012120 1.014 120 (4.28) 4.79 1.45 120 1.008 120 1.008

132 1.005 132 1.006660 (30.52) 39.95 10.40 144 1.004 144 1.00466 (3.05) 4.00 1.04 156 1.002 156 1.003


228 1.000 228 1.001R 2̂= 0.888 0.973 240 1.000 240 1.000

252 1.000 252 1.000264 1.000 264 1.000276 1.000 276 1.000288 1.000 288 1.000




Actual Values Power Model Weibull ModelCurve: Y = Curve: Y =A ̂(B ̂X) 1/ [1-EXP(-A * X ̂B)]

Transformed Values Transformed Values

Total Average

Power Model Weibull ModelFitted Values Fitted Values

GL-8

Intermediate Case StudySummary of Loss Development Projections

Accident EarnedYear Premium Paid Incurred Paid Incurred Paid LDM Inc. LDM Paid LDM Inc. LDM

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

1988 22,122 14,033 14,788 1.075 1.025 15,085 15,147 0.682 0.6851989 26,474 16,972 18,208 1.109 1.039 18,829 18,924 0.711 0.7151990 30,286 19,735 21,465 1.145 1.058 22,595 22,711 0.746 0.7501991 37,741 24,597 27,550 1.196 1.077 29,428 29,674 0.780 0.7861992 45,691 29,409 34,584 1.274 1.096 37,473 37,921 0.820 0.8301993 50,562 30,643 38,965 1.407 1.122 43,106 43,707 0.853 0.8641994 60,349 31,250 44,488 1.621 1.164 50,641 51,799 0.839 0.8581995 75,972 29,611 50,322 2.043 1.237 60,509 62,224 0.796 0.8191996 97,616 27,677 58,061 2.851 1.402 78,898 81,414 0.808 0.8341997 131,861 23,263 64,628 4.627 1.761 107,629 113,822 0.816 0.8631998 168,391 15,073 55,297 11.525 2.855 173,715 157,866 1.032 0.937

Total 747,065 262,263 428,346 637,907 635,212 0.854 0.850

EstimatedUltimate Losses

Estimated UltimateLoss Ratio

Actual Losses@ 12/31/98

Cumulative LDF

GL-9

Intermediate Case StudyApplications of Bornhuetter-Ferguson Technique

AY 1997Paid Paid Incurred

Estimate Estimate Estimate

1. Loss Development Factor to Ultimate 4.627 11.525 2.855

2. Earned Premium 131,861 168,391 168.391

3. Expected Loss Ratio 86% 90% 90%

4. Expected Losses [(2) x (3)] 113,400 151,552 151,522

5. Actual Losses @ 12/31/98 23,263 15,073 55,297

6. Estimated Losses @ 12/31/98(i) Paid or Reported [(4)/(1)] 24,508 13,150 53,085(ii) Unpaid or Unreported [(4) - (6i)] 88,892 138,402 98,467

7. Revised Ultimate Losses [(5) + (6ii)] 112,155 153,475 153,764

AY 1998

GL-10

Intermediate Case StudyEstimated IBNR Reserves

Accident EarnedYear Premium Paid Incurred Paid Incurred Paid LDM Inc. LDM(1) (2) (3) (4) (5) (6) (7) (8)

1988 22,122 15,085 15,147 0.682 0.685 307 3961989 26,474 18,829 18,924 0.711 0.715 621 7161990 30,286 22,595 22,711 0.746 0.750 1,130 1,2461991 37,741 29,428 29,674 0.780 0.786 1,878 2,1241992 45,691 37,473 37,921 0.820 0.830 2,889 3,3371993 50,562 43,106 43,707 0.853 0.864 4,141 4,7421994 60,349 50,641 51,799 0.839 0.858 6,153 7,3111995 75,972 60,509 62,224 0.796 0.819 10,187 11,9021996 97,616 78,898 81,414 0.808 0.834 20,837 23,3531997 131,861 112,153* 113,822 0.851 0.863 47,525 49,1941998 168,391 153,475* 153,764* 0.911 0.913 98,178 98,467

Total 747,065 622,192 631,109 0.833 0.845 193,846 202,763

Selected IBNR RESERVES @ 12/31/98 (AVG of columns 7 & 8) 198,304

* From Bornhuetter-Ferguson Method (Slide GL-10)

Required IBNREstimated

Ultimate LossesSelected

Loss RatioEstimated Ultimate

GL-11

Intermediate Case StudyGLIC’s Carried Reserves

The company’s carried reserves are based upon the straight average of the paid and incurred loss projection methods after application of expected loss techniques.

GL-12

Intermediate Case StudyManagement’s Observations

In previous years, the paid and incurred loss projections were almost identical.

Recently, differences between the two estimates are emerging.

GL-13

Intermediate Case StudyAssignment

GLIC has employed you, a consulting actuary, to complete their 1998 reserve certification and critique the actuarial work done by GLIC’s actuarial department.

GL-14

Intermediate Case StudyInitial Task

You begin the assignment by interviewing the vice president of each of the following insurance disciplines.

Claims Marketing Underwriting

GL-15

Intermediate Case StudyVice President of Claims

Staff and procedures have remained the same for as long as anyone can remember.

Systems have not changed, and there have been no accounting or other changes that would have impacted year-end processing.

GL-16

Intermediate Case StudyVice President of Marketing

The client base is extremely stable.Growth has come primarily from increase in business from existing clients, as opposed to new clients.GLIC’s clients represent almost all US

distributors of Widgets.These clients are expanding into other areas, generating the growth in premium.GL-17

Intermediate Case StudyVice President of Marketing

Given the company’s understanding of the product and their sensible approach to pricing (small annual increases), they have captured and retained their niche market

GL-18

Intermediate Case StudyVice President of UnderwritingThe VP is concerned about the deterioration in the loss ratio (including ALAE) from

81% in 1995 to 91% in 1998 on an accident year basis.

They attribute at least part of the problem to the heavier GL exposures being accepted from their long-term clients.

GL-19

Intermediate Case StudyDistribution of Earned Premium

Accident Year Total Heavy Light % Heavy

1988 22,122 192 21,930 0.9%1989 26,474 822 25,652 3.1%1990 30,286 2,499 27,787 8.3%1991 37,741 5,101 32,640 13.5%1992 45,691 9,987 35,704 21.9%1993 50,562 12,065 38,497 23.9%1994 60,349 15,174 45,175 25.1%1995 75,972 22,537 53,435 29.7%1996 97,616 35,455 62,161 36.3%1997 131,861 59,999 71,862 45.5%1998 168,391 86,337 82,054 51.3%

Total 747,065 250,168 496,897 33.5%

Earned Premium ($000)

GL-20

Intermediate Case StudyVice President of UnderwritingThe underwriting department, with the help of the actuarial staff, will be conducting

separate rate analyses for Heavy GL versus Light GL later in the year.Reports by class of business have just been provided via an ad hoc request to the data processing department.

GL-21

Intermediate Case StudyVice President of UnderwritingAlthough the analysis has not yet been

completed, the underwriting department suspects that Heavy GL rates need to

increase by more than the traditional 5%annual increase taken in previous years for Total GL.

GL-22


Light General LiabilityPaid Loss Development Method

AccidentYear 12 24 36 48 60 72 84 96 108 120 132

1988 $1,329 $3,159 $5,023 $6,902 $8,586 $9,900 $11,682 $12,476 $13,037 $13,454 $13,8851989 1,812 4,177 6,654 9,129 11,420 13,122 14,250 15,134 15,830 16,3371990 1,886 4,517 7,150 9,838 12,543 14,575 16,018 17,075 17,8261991 2,463 5,810 9,220 12,631 15,359 17,647 19,606 20,7631992 2,795 6,565 10,399 14,288 17,831 20,345 22,1761993 2,956 7,012 11,149 15,263 19,384 22,5631994 3,643 8,561 13,535 18,584 22,7651995 3,632 9,331 14,836 20,4441996 4,661 11,154 17,6791997 5,544 13,1281998 10,484

AccidentYear 12-24 24-36 36-48 48-60 60-72 72-84 84-96 96-108 108-120 120-132 132+

1988 2.377 1.590 1.374 1.244 1.153 1.180 1.068 1.045 1.032 1.0321989 2.305 1.593 1.372 1.251 1.149 1.086 1.062 1.046 1.0321990 2.395 1.583 1.376 1.275 1.162 1.099 1.066 1.0441991 2.359 1.587 1.370 1.216 1.149 1.111 1.0591992 2.349 1.584 1.374 1.248 1.141 1.0901993 2.372 1.590 1.369 1.270 1.1641994 2.350 1.581 1.373 1.2251995 2.373 1.590 1.3781996 2.393 1.5851997 2.368

3 Avg. 2.378 1.585 1.373 1.248 1.151 1.100 1.062 1.045 1.032 1.0323 Wtd. 2.378 1.585 1.374 1.246 1.152 1.100 1.062 1.045 1.032 1.0325 Avg. 2.371 1.586 1.373 1.247 1.153 1.113 1.064 1.045 1.032 1.032Mid 3 of 5 2.371 1.586 1.372 1.248 1.153 1.100 1.064 1.045Wtd. 2.367 1.587 1.373 1.245 1.153 1.108 1.063 1.045 1.032 1.032

Selected 2.378 1.601 1.358 1.248 1.153 1.100 1.064 1.045 1.032 1.032

Paid Losses ($000)


GL-23


Total General LiabilityAnalysis of Development Patterns--Paid LossesUsing "The Method of Least Squares"



12 2.378 12 2.48 (0.61) 12 2.010 12 2.38824 1.601 24 (0.14) 3.18 (0.02) 24 1.613 24 1.61636 1.358 36 (0.75) 3.58 0.29 36 1.388 36 1.35048 1.248 48 (1.18) 3.87 0.48 48 1.252 48 1.21960 1.153 60 (1.15) 4.09 0.70 60 1.166 60 1.14572 1.100 72 (1.95) 4.28 0.87 72 1.111 72 1.10084 1.064 84 (2.35) 4.43 1.03 84 1.075 84 1.07096 1.045 96 (2.78) 4.56 1.15 96 1.051 96 1.050

108 1.032 108 (3.12) 4.68 1.25 108 1.035 108 1.036120 1.032 120 (3.46) 4.79 1.25 120 1.024 120 1.026

132 1.016 132 1.019660 (20.71) 39.95 6.39 144 1.011 144 1.01466 (2.07) 4.00 0.64 156 1.008 156 1.011


228 1.001 228 1.001R^2= 0.983 0.997 240 1.001 240 1.001

252 1.000 252 1.001264 1.000 264 1.001276 1.000 276 1.001288 1.000 288 1.000




Actual Values Power Model Weibull ModelCurve: Y = Curve: Y =A ̂(B ̂X) 1/ [1-EXP(-A * X ̂B)]


Total Average

Power Model Weibull ModelFitted Values Fitted Values

GL-24


Light General LiabilityIncurred Loss Development Method

AccidentYear 12 24 36 48 60 72 84 96 108 120 132

1988 5,612 8,794 10,896 12,269 12,932 13,385 13,693 13,926 14,163 14,418 14,6201989 6,752 10,520 13,066 14,738 15,666 16,230 16,603 16,902 17,206 17,5161990 7,642 11,837 14,773 16,649 17,615 18,249 18,650 19,004 19,3461991 9,187 14,561 18,128 20,249 21,464 22,258 22,770 23,1571992 10,611 16,569 20,491 23,073 24,434 25,289 25,8451993 11,775 18,475 22,964 25,857 27,253 28,2891994 13,600 21,311 26,404 29,863 31,7441995 15,388 24,082 29,934 33,5861996 18,143 28,394 35,0381997 21,383 33,6141998 29,195

Accident Year 12-24 24-36 36-48 48-60 60-72 72-84 84-96 96-108 108-120 120-132 132+

1988 1.567 1.239 1.126 1.054 1.035 1.023 1.017 1.017 1.018 1.0141989 1.558 1.242 1.128 1.063 1.036 1.023 1.018 1.018 1.0181990 1.549 1.248 1.127 1.058 1.036 1.022 1.019 1.0181991 1.585 1.245 1.117 1.060 1.037 1.023 1.0171992 1.570 1.230 1.126 1.059 1.035 1.0221993 1.569 1.243 1.126 1.054 1.0381994 1.567 1.239 1.131 1.0631995 1.565 1.243 1.1221996 1.565 1.2341997 1.572

3 Avg. 1.567 1.239 1.126 1.059 1.037 1.022 1.018 1.018 1.018 1.0143 Wtd. 1.568 1.238 1.126 1.059 1.037 1.022 1.018 1.018 1.018 1.0145 Avg. 1.568 1.238 1.124 1.059 1.036 1.023 1.018 1.018 1.018 1.014Mid 3 of 5 1.567 1.239 1.125 1.059 1.036 1.023 1.018 1.018Wtd. 1.568 1.240 1.125 1.059 1.036 1.023 1.018 1.018 1.018 1.014

Selected 1.567 1.239 1.126 1.059 1.037 1.022 1.018 1.018 1.018 1.014



GL-25


Light General LiabilityAnalysis of Development Patterns--Incurred LossesUsing "The Method of Least Squares"



12 1.567 12 (0.80) 2.48 0.02 12 1.283 12 1.51024 1.239 24 (1.54) 3.18 0.50 24 1.186 24 1.22436 1.126 36 (2.13) 3.58 0.78 36 1.124 36 1.12448 1.059 48 (2.86) 3.87 1.06 48 1.084 48 1.07560 1.037 60 (3.32) 4.09 1.20 60 1.057 60 1.04972 1.022 72 (3.83) 4.28 1.35 72 1.038 72 1.03384 1.018 84 (4.03) 4.43 1.40 84 1.026 84 1.02396 1.018 96 (4.03) 4.56 1.40 96 1.018 96 1.016

108 1.018 108 (4.03) 4.68 1.40 108 1.012 108 1.011120 1.014 120 (4.28) 4.79 1.45 120 1.008 120 1.008

132 1.060 132 1.006660 (30.83) 39.95 10.55 144 1.004 144 1.00566 (3.08) 4.00 1.05 156 1.003 156 1.003


228 1.000 228 1.001R^2= 0.884 0.972 240 1.000 240 1.001

252 1.000 252 1.000264 1.000 264 1.000276 1.000 276 1.000288 1.000 288 1.000300 1.000 300 1.000




AverageTotal


Transformed Values Weibull ModelFitted Values

A ̂(B ̂X)

Actual Values

1/ [1-EXP(-A * X ̂B)]


Transformed Values

GL-26

Intermediate Case StudyBornhuetter-Ferguson Technique - Light GL

Paid IncurredEstimate Estimate

1. Loss Development Factor 10.446 2.690

2. Earned Premium 82,054 82,054

3. Expected Loss Ratio 83.5% 83.5%

4. Expected Losses [(2) x (3)] 68,515 68,515

5. Actual Losses @ 12/31/98 10,484 29,195

6. Estimated Losses @ 12/31/98(I) Paid or Reported [(4) / (1)] 6,546 25,467(ii) Unpaid or Unreported [(4) - (6i)] 61,969 43,048

7. Revised Ultimate Losses [(5)+ (6ii)] 72,453 72,243

Accident Year 1998

GL-27

Intermediate Case StudyIBNR Reserves Estimate - Light GL

Accident EarnedYear Premium Paid Incurred Paid Incurred Paid LDM Inc. LDM

(1) (2) (3) (4) (5) (6) (7) (8)

1988 21,930 14,996 14,986 0.684 0.683 376 3661989 25,652 18,209 18,205 0.710 0.710 693 6891990 2,787 20,504 20,504 0.738 0.737 1,158 1,1231991 32,640 24,957 24,942 0.765 0.764 1,800 1,7851992 35,704 28,361 28,339 0.794 0.794 2,516 2,4941993 358,497 31,742 31,701 0.825 0.823 3,453 3,4121994 45,175 36,926 36,889 0.817 0.817 5,182 5,1451995 53,435 41,385 41,332 0.774 0.774 7,799 7,7461996 62,161 48,600 48,552 0.782 0.781 13,562 13,5141997 71,862 57,779 57,711 0.804 0.803 24,165 24,0971998 82,054 72,453* 72,243* 0.883 0.880 43,258 43,048

Total 496,897 395,912 395,369 0.797 0.796 103,962 103,419

1988-96 342,981 265,680 265,415 0.775 0.774 36,539 36,274

* From Bornhuetter-Ferguson Method (Slide GL-27)


EstimatedLoss Ratio

EstimatedRequired IBNR

GL-28


Heavy General LiabilityPaid Loss Development Method

AccidentYear 12 24 36 48 60 72 84 96 108 120 132

1988 11 29 49 71 91 108 120 130 137 142 1481989 45 120 210 309 400 472 533 576 609 6351990 138 374 640 935 1,249 1,496 1,677 1,811 1,9091991 318 845 1,451 2,107 2,663 3,148 3,573 3,8341992 644 1,707 2,926 4,263 5,555 6,516 7,2331993 758 2,027 3,489 5,063 6,733 8,0801994 1,009 2,675 4,574 6,655 8,4851995 1,360 3,643 6,270 9,1671996 2,157 5,830 9,9981997 3,793 10,1351998 4,589

Accident Year 12-24 24-36 36-48 48-60 60-72 72-84 84-96 96-108 108-120 120-132 132+

1988 2.636 1.690 1.449 1.282 1.187 1.111 1.083 1.054 1.036 1.0421989 2.667 1.750 1.471 1.294 1.180 1.129 1.081 1.057 1.0431990 2.710 1.711 1.461 1.336 1.980 1.121 1.080 1.0541991 2.657 1.717 1.520 1.264 1.182 1.135 1.0731992 2.651 1.714 1.457 1.303 1.173 1.1101993 2.674 1.721 1.451 1.330 1.2001994 2.651 1.710 1.455 1.2751995 2.679 1.721 1.4621996 2.703 1.7151997 2.672

3 Avg. 2.685 1.715 1.456 1.303 1.185 1.122 1.078 1.055 1.040 1.0423 Wtd. Avg. 2.682 1.716 1.457 1.300 1.187 1.119 1.076 1.055 1.042 1.0425 Avg. 2.676 1.716 1.455 1.302 1.187 1.121 1.079 1.055 1.040 1.042Mid 3 of 5 2.675 1.717 1.455 1.303 1.187 1.120 1.08 1.054Wtd. Avg. 2.676 1.716 1.457 1.298 1.187 1.119 1.076 1.055 1.042 1.042

Selected 2.684 1.717 1.456 1.303 1.187 1.122 1.078 1.055 1.04 1.039


Paid Losses ($000)

GL-29


Heavy General LiabilityAnalysis of Development Patterns--Paid LossesUsing "The Method of Least Squares"



12 2.684 12 (0.01) 2.48 (0.76) 12 2.241 12 2.72424 1.717 24 (0.62) 3.18 (0.14) 24 1.738 24 1.76136 1.456 36 (0.98) 3.58 0.15 36 1.461 36 1.43348 1.303 48 (1.33) 3.87 0.38 48 1.297 48 1.27360 1.187 60 (1.76) 4.09 0.61 60 1.195 60 1.18272 1.122 72 (2.16) 4.28 0.80 72 1.130 72 1.12684 1.078 84 (2.59) 4.43 0.97 84 1.087 84 1.08896 1.055 96 (2.93) 4.56 1.08 96 1.059 96 1.063

108 1.040 108 (3.24) 4.68 1.18 108 1.040 108 1.046120 1.039 120 (3.26) 4.79 1.19 120 1.027 120 1.033

132 1.019 132 1.025660 (18.88) 39.95 5.46 144 1.013 144 1.01866 (1.89) 4.00 0.55 156 1.009 156 1.014


228 1.001 228 1.002R^2= 0.985 0.996 240 1.001 240 1.002

252 1.000 252 1.001264 1.000 264 1.001276 1.000 276 1.001288 1.000 288 1.001300 1.000 300 1.000





A ̂(B ̂X)

Actual Values

1/ [1-EXP(-A * X ̂B)]


AverageTotal



GL-30


Heavy General LiabilityIncurred Loss Development Method

AccidentYear 12 24 36 48 60 72 84 96 108 120 132

1988 50 85 110 127 135 141 145 149 152 155 1581989 223 377 490 565 605 631 649 663 677 6921990 703 1,175 1,531 1,768 1,892 1,975 2,027 2,073 2,1191991 1,465 2,512 3,263 3,729 4,005 4,185 4,303 4,3931992 3,036 5,148 6,595 7,611 8,166 8,518 8,7391993 3,774 6,397 8,297 9,575 10,207 10,6761994 4,660 7,889 10,201 11,833 12,7441995 6,641 11,230 14,566 16,7361996 10,587 17,903 23,0231997 18,254 31,0141998 26,102

Accident Year 12-24 24-36 36-48 48-60 60-72 72-84 84-96 96-108 108-120 120-132 132+

1988 1.700 1.294 1.155 1.063 1.044 1.028 1.028 1.020 1.020 1.0191989 1.691 1.300 1.153 1.071 1.043 1.029 1.022 1.021 1.0221990 1.671 1.303 1.155 1.070 1.044 1.026 1.023 1.0221991 1.715 1.299 1.143 1.074 1.045 1.028 1.0211992 1.696 1.281 1.154 1.073 1.043 1.0261993 1.695 1.297 1.154 1.066 1.0461994 1.693 1.293 1.160 1.0771995 1.691 1.297 1.1491996 1.691 1.2861997 1.699

3 Avg. 1.694 1.292 1.154 1.072 1.045 1.027 1.022 1.021 1.021 1.0193 Wtd. 1.695 1.291 1.154 1.072 1.045 1.027 1.021 1.022 1.022 1.0195 Avg. 1.694 1.291 1.152 1.072 1.044 1.027 1.023 1.021 1.021 1.019Mid 3 of 5 1.693 1.292 1.152 1.072 1.044 1.028 1.022 1.021Wtd. Avg. 1.695 1.291 1.153 1.072 1.045 1.027 1.022 1.021 1.022 1.019

Selected 1.694 1.292 1.154 1.072 1.044 1.027 1.022 1.022 1.022 1.017



GL-31


Heavy General LiabilityAnalysis of Development Patterns -- Incurred LossesUsing "The Method of Least Squares"



12 1.694 12 (0.64) 2.48 (0.11) 12 1.344 12 1.62524 1.292 24 (1.36) 3.18 0.40 24 1.225 24 1.27536 1.154 36 (1.94) 3.58 0.70 36 1.149 36 1.15248 1.072 48 (2.67) 3.87 0.99 48 1.100 48 1.09360 1.044 60 (3.15) 4.09 1.15 60 1.067 60 1.06072 1.027 72 (3.63) 4.28 1.29 72 1.046 72 1.04084 1.022 84 (3.83) 4.43 1.35 84 1.031 84 1.02896 1.022 96 (3.83) 4.56 1.35 96 1.021 96 1.020

108 1.022 108 (3.83) 4.68 1.35 108 1.014 108 1.014120 1.017 120 (4.08) 4.79 1.41 120 1.010 120 1.010

132 1.007 132 1.007660 (28.95) 39.95 9.87 144 1.005 144 1.00566 (2.89) 4.00 0.99 156 1.003 156 1.004


228 1.000 228 1.001R 2̂= 0.885 0.971 240 1.000 240 1.001

252 1.000 252 1.000264 1.000 264 1.000276 1.000 276 1.000288 1.000 288 1.000300 1.000 300 1.000





A ̂(B ̂X)

Actual Values

1/ [1-EXP(-A * X ̂B)]


AverageTotal


Transformed ValuesTransformed Values

GL-32

Intermediate Case StudyBornhuetter-Ferguson Technique - Heavy GL

Paid IncurredEstimate Estimate

1. Loss Development Factor 15.74 3.25

2. Earned Premium 86,337 86,337

3. Expected Loss Ratio 102.0% 102.0%

4. Expected Losses [(2) x (3)] 88,064 88,064

5. Actual Losses @ 12/31/98 4,589 26,102

6. Estimated Losses @ 12/31/98(I) Paid or Reported [(4) / (1)] 5,595 27,129(ii) Unpaid or Unreported [(4) - (6i)] 82,469 60,934

7. Revised Ultimate Losses [(5)+ (6ii)] 87,058 87,036

Accident Year 1998

GL-33

Intermediate Case StudyIBNR Reserve Estimate - Heavy GL

Accident EarnedYear Premium Paid Incurred Paid Incurred Paid LDM Inc. LDM

(1) (2) (3) (4) (5) (6) (7) (8)

1988 192 163 163 0.849 0.849 5 51989 822 726 725 0.883 0.882 34 331990 2,499 2,269 2,269 0.908 0.908 150 1501991 5,101 4,808 4,806 0.943 0.942 415 4131992 9,987 9,778 9,772 0.979 0.979 1,039 1,0331993 12,065 12,255 12,260 1.016 1.016 1,579 1,5841994 15,174 15,276 15,279 1.007 1.007 2,532 2,5351995 22,537 21,504 21,509 0.954 0.954 4,768 4,7731996 35,455 34,149 34,146 0.963 0.963 11,126 11,1231997 59,999 59,437 59,430 0.991 0.991 28,423 28,4161998 86,337 87,058* 87,036* 0.837 0.981 60,956 60,934

Total 250168 160365 160359 0.954 0.954 111,027 110,999

1988-96 103,832 100,928 100,929 0.991 0.991 21,648 21,649

* From Bornhutter-Ferguson Method (Slide GL-33)


EstimatedRequired IBNR

Estimated UltimateLoss Ratio

GL-34

Intermediate Case StudySummary of IBNR Estimates

Paid IncurredEstimates Estimates

Total General Liability 193,846 202,763

Sum of ComponentsHeavy GL 111,027 110,999Light GL 103,962 103,419Total GL 214,989 214,419

Selected by Consulting Actuary

GLIC's Carried IBNR Reserves (Slide GL-11)

Indicated Deficiency @ 12/31/98

214,704

198,304

(16,399)

GL-35

Intermediate Case StudyBalance Sheet @ 12/31/98 ($000)

Bonds $463,388 Loss & LAE ReservesCase Reserves $208,052

Stocks $48,262 IBNR Reserves $214,704 *

Cash $11,028 Unearned Premium Reserve $84,196

Total Invested Assets $522,678 Other Liabilities $24,965

Agents' Balance $19,799 Total Liabilities $531,917 *

Other Assets $35,662 Policyholders' Surplus $46,223 *

Total Assets $578,139 Total Liabilities & Surplus $578,139

*Changes from slide GL-2

Assets Liabilities & Surplus

GL-36

1999 clrs intermediate case study discussion material for gl insurance company

Documents

year simple average2

year volume weighted

development factorsyear12

ldmpaid ldminc

yearsstable book of

bx var

selecte factors2