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Transcript of Estimating ULAE Liabilities Alejandra Nolibos April 12, 2005 Rediscovering and Expanding Kittel’s...
![Page 1: Estimating ULAE Liabilities Alejandra Nolibos April 12, 2005 Rediscovering and Expanding Kittel’s Approach By: Robert F. Conger and Alejandra Nolibos.](https://reader036.fdocuments.us/reader036/viewer/2022070415/5697bf9b1a28abf838c92b4d/html5/thumbnails/1.jpg)
Estimating ULAE Liabilities
Alejandra NolibosApril 12, 2005
Rediscovering and Expanding Kittel’s Approach
By: Robert F. Conger and Alejandra Nolibos
![Page 2: Estimating ULAE Liabilities Alejandra Nolibos April 12, 2005 Rediscovering and Expanding Kittel’s Approach By: Robert F. Conger and Alejandra Nolibos.](https://reader036.fdocuments.us/reader036/viewer/2022070415/5697bf9b1a28abf838c92b4d/html5/thumbnails/2.jpg)
2
Discussion Outline
The Problem
The Specific Solution — ULAE Ratio
Generalized Solution — ULAE Ratio
ULAE Reserves — Three Methods
The Weighting Parameters
Difficulties and Possible Refinements
![Page 3: Estimating ULAE Liabilities Alejandra Nolibos April 12, 2005 Rediscovering and Expanding Kittel’s Approach By: Robert F. Conger and Alejandra Nolibos.](https://reader036.fdocuments.us/reader036/viewer/2022070415/5697bf9b1a28abf838c92b4d/html5/thumbnails/3.jpg)
The Problem
XYZ Company ULAE Reserve for Workers Compensation
![Page 4: Estimating ULAE Liabilities Alejandra Nolibos April 12, 2005 Rediscovering and Expanding Kittel’s Approach By: Robert F. Conger and Alejandra Nolibos.](https://reader036.fdocuments.us/reader036/viewer/2022070415/5697bf9b1a28abf838c92b4d/html5/thumbnails/4.jpg)
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The Problem: XYZ Company ULAE Reserves
Standard paid-to-paid ratios not well behaved
Traditional 50/50 assumption not appropriate
Count-based methods not feasible
![Page 5: Estimating ULAE Liabilities Alejandra Nolibos April 12, 2005 Rediscovering and Expanding Kittel’s Approach By: Robert F. Conger and Alejandra Nolibos.](https://reader036.fdocuments.us/reader036/viewer/2022070415/5697bf9b1a28abf838c92b4d/html5/thumbnails/5.jpg)
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Standard paid-to-paid ratios not well behavedXYZ Company — Workers’ Comp
1999
2000
2001
2002
2003
2004
Total
Calendar Year
$1,978
4,820
8,558
12,039
13,143
15,286
$55,824
$4,590
14,600
38,390
58,297
86,074
105,466
$307,417
.431
.330
.223
.207
.153
.145
.182
Cal. Year Paid ULAE
Cal. Year Paid Loss & ALAE
Paid-to-Paid ULAE Ratio
(1) (2) (3) (4) = (2)/(3)
![Page 6: Estimating ULAE Liabilities Alejandra Nolibos April 12, 2005 Rediscovering and Expanding Kittel’s Approach By: Robert F. Conger and Alejandra Nolibos.](https://reader036.fdocuments.us/reader036/viewer/2022070415/5697bf9b1a28abf838c92b4d/html5/thumbnails/6.jpg)
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The Problem: XYZ Company ULAE Reserves
Standard paid-to-paid ratios not well behaved
Traditional 50/50 assumption not appropriate
Count-based methods not feasible
![Page 7: Estimating ULAE Liabilities Alejandra Nolibos April 12, 2005 Rediscovering and Expanding Kittel’s Approach By: Robert F. Conger and Alejandra Nolibos.](https://reader036.fdocuments.us/reader036/viewer/2022070415/5697bf9b1a28abf838c92b4d/html5/thumbnails/7.jpg)
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Traditional 50/50 assumption for ULAE payments
As stated:
As typicallyapplied:
or
50% when claimis reported
50% when claimis reported
50% as claim $ recorded
50% whenclaim is closed
50% as claim$ closed
50% as claim $ paid
![Page 8: Estimating ULAE Liabilities Alejandra Nolibos April 12, 2005 Rediscovering and Expanding Kittel’s Approach By: Robert F. Conger and Alejandra Nolibos.](https://reader036.fdocuments.us/reader036/viewer/2022070415/5697bf9b1a28abf838c92b4d/html5/thumbnails/8.jpg)
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Traditional 50/50 assumption for ULAE payments
As stated:
As typicallyapplied:
or
XYZ Company
50% when claimis reported
50% when claimis reported
50% as claim $ recorded
60% – 70% when claim is reported
50% whenclaim is closed
50% as claim$ closed
50% as claim$ paid
30% – 40% as claim $ paid
Larger claims require proportionately more ULAE than small claims
![Page 9: Estimating ULAE Liabilities Alejandra Nolibos April 12, 2005 Rediscovering and Expanding Kittel’s Approach By: Robert F. Conger and Alejandra Nolibos.](https://reader036.fdocuments.us/reader036/viewer/2022070415/5697bf9b1a28abf838c92b4d/html5/thumbnails/9.jpg)
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Traditional 50/50 assumption for ULAE payments
Other potential departures from traditional assumption:
Significant ULAE for other claim activities (e.g., reopening)
ULAE split other than 50/50
ULAE $ not varying by claim size
![Page 10: Estimating ULAE Liabilities Alejandra Nolibos April 12, 2005 Rediscovering and Expanding Kittel’s Approach By: Robert F. Conger and Alejandra Nolibos.](https://reader036.fdocuments.us/reader036/viewer/2022070415/5697bf9b1a28abf838c92b4d/html5/thumbnails/10.jpg)
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The Problem: XYZ Company ULAE Reserves
Standard paid-to-paid ratios not well behaved
Traditional 50/50 assumption not appropriate
Count-based methods not feasible
![Page 11: Estimating ULAE Liabilities Alejandra Nolibos April 12, 2005 Rediscovering and Expanding Kittel’s Approach By: Robert F. Conger and Alejandra Nolibos.](https://reader036.fdocuments.us/reader036/viewer/2022070415/5697bf9b1a28abf838c92b4d/html5/thumbnails/11.jpg)
The Specific Solution
XYZ Company ULAE Ratio
![Page 12: Estimating ULAE Liabilities Alejandra Nolibos April 12, 2005 Rediscovering and Expanding Kittel’s Approach By: Robert F. Conger and Alejandra Nolibos.](https://reader036.fdocuments.us/reader036/viewer/2022070415/5697bf9b1a28abf838c92b4d/html5/thumbnails/12.jpg)
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ULAE Ratio DerivationXYZ Company — Workers’ Comp
Paid ULAE $ =
[ULAE ratio] x [60% to 70%] x [L + A $ on claims reported] +
[ULAE ratio] x [30% to 40%] x [L + A $ paid]
ULAE Ratio = Paid ULAE $ /
[60% to 70%] x [L + A $ on claims reported] +[30% to 40%] x [L + A $ paid]
CALENDAR YEARWe believe:
Therefore:
![Page 13: Estimating ULAE Liabilities Alejandra Nolibos April 12, 2005 Rediscovering and Expanding Kittel’s Approach By: Robert F. Conger and Alejandra Nolibos.](https://reader036.fdocuments.us/reader036/viewer/2022070415/5697bf9b1a28abf838c92b4d/html5/thumbnails/13.jpg)
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ULAE Ratio CalculationXYZ Company — Workers’ Comp
$4,590
14,600
38,390
58,297
86,074
105,466
$307,417
1999
2000
2001
2002
2003
2004
Total
$1,978
4,820
8,558
12,039
13,143
15,286
$55,824
$27,200
76,700
106,900
154,300
163,100
176,400
$704,600
$18,156
51,860
79,496
115,899
132,290
148,026
$545,727
.109
.093
.108
.104
.099
.103
.102
Cal. Year PaidLoss & ALAE
(4)
Calendar Year
(1)
Cal. Year Paid ULAE
Est. RYUltimate
Loss & ALAE(2) (3)
Loss Basis ULAE Ratio
(5*) (6)=(2)/(5)
*(5) = 60% x (3) + 40% x (4)
60/40 ASSUMPTION
Projected AY Ultimate Loss + ALAE = $713,400
![Page 14: Estimating ULAE Liabilities Alejandra Nolibos April 12, 2005 Rediscovering and Expanding Kittel’s Approach By: Robert F. Conger and Alejandra Nolibos.](https://reader036.fdocuments.us/reader036/viewer/2022070415/5697bf9b1a28abf838c92b4d/html5/thumbnails/14.jpg)
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.109
.093
.108
.104
.099
.103
.102
ULAE Ratio60/40 Weights
ULAE Ratio — Sensitivity to Weights XYZ Company — Workers’ Comp
1999
2000
2001
2002
2003
2004
Total
Calendar Year
.097
.083
.099
.096
.094
.099
.095
ULAE Ratio70/30 Weights
Selected .100
![Page 15: Estimating ULAE Liabilities Alejandra Nolibos April 12, 2005 Rediscovering and Expanding Kittel’s Approach By: Robert F. Conger and Alejandra Nolibos.](https://reader036.fdocuments.us/reader036/viewer/2022070415/5697bf9b1a28abf838c92b4d/html5/thumbnails/15.jpg)
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Standard paid-to-paid ratios not well behavedXYZ Company — Workers’ Comp
1999
2000
2001
2002
2003
2004
Total
Calendar Year
$1,978
4,820
8,558
12,039
13,143
15,286
$55,824
$4,590
14,600
38,390
58,297
86,074
105,466
$307,417
.431
.330
.223
.207
.153
.145
.182
Cal. Year Paid ULAE
Cal. Year Paid Loss & ALAE
Paid-to-Paid ULAE Ratio
(1) (2) (3) (4) = (2)/(3)
![Page 16: Estimating ULAE Liabilities Alejandra Nolibos April 12, 2005 Rediscovering and Expanding Kittel’s Approach By: Robert F. Conger and Alejandra Nolibos.](https://reader036.fdocuments.us/reader036/viewer/2022070415/5697bf9b1a28abf838c92b4d/html5/thumbnails/16.jpg)
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An acceptable simplification?
UltimateL+A $ on claims reported during calendar period
UltimateL+A $ on claims occurring during calendar/accident period
UltimateL+A $ on claims occurring during calendar/accident period
Pure IBNR during period–
=
?UltimateL+A $ on claims reported during calendar period
![Page 17: Estimating ULAE Liabilities Alejandra Nolibos April 12, 2005 Rediscovering and Expanding Kittel’s Approach By: Robert F. Conger and Alejandra Nolibos.](https://reader036.fdocuments.us/reader036/viewer/2022070415/5697bf9b1a28abf838c92b4d/html5/thumbnails/17.jpg)
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Paid losses during period
Case reserves during period
Kittel’s simplification
UltimateL+A $ on claims reported during calendar period
Paid losses during period
Case reserves during period +
=
?
Note: Kittel also assumes: - Payment = Closing - 50/50 Weights
IBNR during period
UltimateL+A $ on claims reported during calendar period
+
+
![Page 18: Estimating ULAE Liabilities Alejandra Nolibos April 12, 2005 Rediscovering and Expanding Kittel’s Approach By: Robert F. Conger and Alejandra Nolibos.](https://reader036.fdocuments.us/reader036/viewer/2022070415/5697bf9b1a28abf838c92b4d/html5/thumbnails/18.jpg)
Generalized Solution – ULAE Ratio
![Page 19: Estimating ULAE Liabilities Alejandra Nolibos April 12, 2005 Rediscovering and Expanding Kittel’s Approach By: Robert F. Conger and Alejandra Nolibos.](https://reader036.fdocuments.us/reader036/viewer/2022070415/5697bf9b1a28abf838c92b4d/html5/thumbnails/19.jpg)
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Generalized solution — ULAE ratio
% of Ultimate ULAE Spent
U1% opening claims
U2% maintaining claims
U3% closing claims
Modeling Based On:
Ultimate cost of claims reported during period
Claim payments during period
Ultimate cost of claims closed during period
Note: U1 + U2 + U3 = 100%
![Page 20: Estimating ULAE Liabilities Alejandra Nolibos April 12, 2005 Rediscovering and Expanding Kittel’s Approach By: Robert F. Conger and Alejandra Nolibos.](https://reader036.fdocuments.us/reader036/viewer/2022070415/5697bf9b1a28abf838c92b4d/html5/thumbnails/20.jpg)
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Generalized solution — ULAE ratio
[ULAE $ Paid During Period]
U1% x
/
Note: U1 + U2 + U3 = 100%
U2% x
U3% x
Ultimate cost of claims reported during period
Claim payments during period
Ultimate cost of claims closed during period
+
+
![Page 21: Estimating ULAE Liabilities Alejandra Nolibos April 12, 2005 Rediscovering and Expanding Kittel’s Approach By: Robert F. Conger and Alejandra Nolibos.](https://reader036.fdocuments.us/reader036/viewer/2022070415/5697bf9b1a28abf838c92b4d/html5/thumbnails/21.jpg)
ULAE Reserves – Three Methods
![Page 22: Estimating ULAE Liabilities Alejandra Nolibos April 12, 2005 Rediscovering and Expanding Kittel’s Approach By: Robert F. Conger and Alejandra Nolibos.](https://reader036.fdocuments.us/reader036/viewer/2022070415/5697bf9b1a28abf838c92b4d/html5/thumbnails/22.jpg)
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ULAE Reserves — Three Methods
[Expected Ultimate] minus [Paid]
[Expected unpaid]
Multiple of [Paid to date]
All three methods use the selected ULAE ratio
![Page 23: Estimating ULAE Liabilities Alejandra Nolibos April 12, 2005 Rediscovering and Expanding Kittel’s Approach By: Robert F. Conger and Alejandra Nolibos.](https://reader036.fdocuments.us/reader036/viewer/2022070415/5697bf9b1a28abf838c92b4d/html5/thumbnails/23.jpg)
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ULAE Ratio CalculationXYZ Company — Workers Comp
$4,590
14,600
38,390
58,297
86,074
105,466
$307,417
1999
2000
2001
2002
2003
2004
Total
$1,978
4,820
8,558
12,039
13,143
15,286
$55,824
$27,200
76,700
106,900
154,300
163,100
176,400
$704,600
$18,156
51,860
79,496
115,899
132,290
148,026
$545,727
.109
.093
.108
.104
.099
.103
.102
Cal. Year PaidLoss & ALAE
(4)
Calendar Year
(1)
Cal. Year Paid ULAE
Est. RYUltimate
Loss & ALAE(2) (3)
Loss Basis ULAE Ratio
(5*) (6)=(2)/(5)
*(5) = 60% x (3) + 40% x (4)
60/40 ASSUMPTION
Projected AY Ultimate Loss + ALAE = $713,400
![Page 24: Estimating ULAE Liabilities Alejandra Nolibos April 12, 2005 Rediscovering and Expanding Kittel’s Approach By: Robert F. Conger and Alejandra Nolibos.](https://reader036.fdocuments.us/reader036/viewer/2022070415/5697bf9b1a28abf838c92b4d/html5/thumbnails/24.jpg)
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ULAE Reserves — Three Methods
Accident year loss + ALAEKey totals
Projected Ultimate $713,400
Pure IBNR 8,800
Projected Ultimate on known claims 704,600
Paid loss + ALAE 307,417
Loss basis(60% x 704,600) + (40% x 307,417) 545,727
Paid ULAE 55,824
Selected ULAE Ratio .100
60/40 ASSUMPTION
![Page 25: Estimating ULAE Liabilities Alejandra Nolibos April 12, 2005 Rediscovering and Expanding Kittel’s Approach By: Robert F. Conger and Alejandra Nolibos.](https://reader036.fdocuments.us/reader036/viewer/2022070415/5697bf9b1a28abf838c92b4d/html5/thumbnails/25.jpg)
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ULAE Reserves — Three Methods
ULAE Reserve
Expected ultimate minus paid:(.10 x 713,400) – (55,824) = 15,516
Expected unpaid:(.10) x (713,400 – 545,727) = 16,767
Multiple of paid to date:55,824 x (713,400 ÷ 545,727 – 1.0) = 17,152
60/40 ASSUMPTION
![Page 26: Estimating ULAE Liabilities Alejandra Nolibos April 12, 2005 Rediscovering and Expanding Kittel’s Approach By: Robert F. Conger and Alejandra Nolibos.](https://reader036.fdocuments.us/reader036/viewer/2022070415/5697bf9b1a28abf838c92b4d/html5/thumbnails/26.jpg)
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ULAE Reserves — Three MethodsXYZ Company — Workers’ Comp
Expected ultimate minus 15,51615,516
paid
Expected unpaid 16,76712,795
Multiple of paid to date 17,15212,201
60/40 Assumption
70/30Assumption
Using ULAE ratio = .100
![Page 27: Estimating ULAE Liabilities Alejandra Nolibos April 12, 2005 Rediscovering and Expanding Kittel’s Approach By: Robert F. Conger and Alejandra Nolibos.](https://reader036.fdocuments.us/reader036/viewer/2022070415/5697bf9b1a28abf838c92b4d/html5/thumbnails/27.jpg)
The Weighting Parameters
![Page 28: Estimating ULAE Liabilities Alejandra Nolibos April 12, 2005 Rediscovering and Expanding Kittel’s Approach By: Robert F. Conger and Alejandra Nolibos.](https://reader036.fdocuments.us/reader036/viewer/2022070415/5697bf9b1a28abf838c92b4d/html5/thumbnails/28.jpg)
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U1, U2, and U3
Interviews
“Time and Motion” studies
Computer-based activity analysis
Sensitivity testing
![Page 29: Estimating ULAE Liabilities Alejandra Nolibos April 12, 2005 Rediscovering and Expanding Kittel’s Approach By: Robert F. Conger and Alejandra Nolibos.](https://reader036.fdocuments.us/reader036/viewer/2022070415/5697bf9b1a28abf838c92b4d/html5/thumbnails/29.jpg)
Difficulties and Potential Refinements
![Page 30: Estimating ULAE Liabilities Alejandra Nolibos April 12, 2005 Rediscovering and Expanding Kittel’s Approach By: Robert F. Conger and Alejandra Nolibos.](https://reader036.fdocuments.us/reader036/viewer/2022070415/5697bf9b1a28abf838c92b4d/html5/thumbnails/30.jpg)
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Potential Refinements
Can add additional activities (e.g., reopening) Need $ measure of volume Select weight
Replace $ with counts to produce Wendy-Johnson method [ULAE effort not related to size of claim]
Stratify claims into subpopulations for which ULAE is “strictly” proportional to claim size or ULAE is “strictly” independent of claim size
![Page 31: Estimating ULAE Liabilities Alejandra Nolibos April 12, 2005 Rediscovering and Expanding Kittel’s Approach By: Robert F. Conger and Alejandra Nolibos.](https://reader036.fdocuments.us/reader036/viewer/2022070415/5697bf9b1a28abf838c92b4d/html5/thumbnails/31.jpg)
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Other Difficulties
Changing definitions of LAE
ULAE resource needs vary over the life of claim
Inflation