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AS463_Lec02
Course: ACTSC 463, Fall 2011School: Waterloo
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463/863 Property ACTSC and Casualty Loss Reserving 1 Development Triangles 2 Exercises > Calculate the CY 2007 incurred losses > Calculate the runoff in 2006 > Derive the RY incurred loss triangle Claim Snap Shot Claim # 1 2 3 4 5 6 7 8 9 10 Acc Date 12-Jan-05 10-Mar-05 01-Nov-05 13-Feb-06 01-Dec-06 16-Jan-07 05-May-07 29-Jul-07 13-Sep-07 05-Jun-08 Rep Date 12-Apr-05 12-Apr-05 30-Jan-06...
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463/863
Property ACTSC and Casualty
Loss Reserving
1
Development Triangles
2
Exercises
> Calculate the CY 2007 incurred losses
> Calculate the runoff in 2006
> Derive the RY incurred loss triangle
Claim Snap Shot
Claim #
1
2
3
4
5
6
7
8
9
10
Acc Date
12-Jan-05
10-Mar-05
01-Nov-05
13-Feb-06
01-Dec-06
16-Jan-07
05-May-07
29-Jul-07
13-Sep-07
05-Jun-08
Rep Date
12-Apr-05
12-Apr-05
30-Jan-06
14-May-06
01-Mar-07
16-Apr-07
28-May-07
21-Aug-07
06-Oct-07
28-Jun-08
2005
Paid
200
0
Case
300
1000
3
2006
Paid
500
0
0
600
Case
200
1000
500
0
2007
Paid
700
800
500
600
150
320
0
400
0
Case
0
500
0
0
350
100
450
100
1000
2008
Paid
700
800
500
600
300
400
0
400
0
500
Case
0
500
0
0
0
0
550
100
1000
500
Solutions
2007
= 2370 + 1100 600
+ 2500 2200 = 3170
2006 = 2005 2006 = 700
Incurred Triangle
RY/DY
12
24
36
48
2005
1500
1700
2000
2000
2006
1100
1100
1100
2007
2870
2750
2008
1000
4
Common Triangles
>
>
>
>
>
>
= +
=
>
=
=
=
>
>
5
Common Triangles
=
> =
>
> =
6
Triangle Diagnostics
7
Diagnostics - Paid
Accident
Year
12
24
36
48
60
72
84
96
108
120
2000
9,963
22,052
28,799
33,078
36,230
38,920
40,597
41,866
42,466
43,471
2001
8,966
20,810
26,581
30,660
32,798
34,243
36,302
37,766
40,494
2002
8,272
20,316
25,102
28,122
31,064
33,540
36,164
39,367
2003
8,755
16,754
20,719
23,704
26,925
30,351
32,457
2004
5,559
14,197
19,415
23,282
28,624
32,334
2005
7,260
19,115
27,020
33,300
39,040
2006
8,626
30,671
45,235
53,797
2007
14,305
44,924
62,035
2008
19,323
60,057
2009
26,034
> Growth in book?
> Claim deterioration?
> Rate of settlement?
8
Diagnostics - Incurred
Accident
Year
12
24
36
48
60
72
84
96
108
120
2000
61,308
48,529
48,609
48,302
48,512
48,809
50,399
50,936
51,186
52,119
2001
45,314
40,353
38,142
37,826
38,565
39,469
41,285
43,630
44,135
2002
36,566
34,412
33,061
34,556
36,336
40,546
41,570
42,069
2003
33,804
27,736
29,823
31,605
35,173
36,074
36,092
2004
28,415
27,781
29,657
34,648
37,101
37,076
2005
42,399
41,075
46,552
52,263
54,852
2006
52,838
64,693
67,769
75,499
2007
66,955
82,524
90,873
2008
79,705
101,549
2009
90,441
>
>
>
>
Growth in book?
Claim deterioration?
Rate of settlement?
Case strengthening?
9
Diagnostics Paid to Incurred
Accident
Year
12
24
36
48
60
72
84
96
108
120
2000
0.163
0.454
0.592
0.685
0.747
0.797
0.806
0.822
0.830
0.834
2001
0.198
0.516
0.697
0.811
0.850
0.868
0.879
0.866
0.918
2002
0.226
0.590
0.759
0.814
0.855
0.827
0.870
0.936
2003
0.259
0.604
0.695
0.750
0.765
0.841
0.899
2004
0.196
0.511
0.655
0.672
0.772
0.872
2005
0.171
0.465
0.580
0.637
0.712
2006
0.163
0.474
0.667
0.713
2007
0.214
0.544
0.683
2008
0.242
0.591
2009
0.288
> Rate of settlement?
> Case reserve weakening?
10
Diagnostics - Reported
Accident
Year
12
24
36
48
60
72
84
96
108
120
2000
7,074
6,891
6,882
6,862
6,868
6,865
6,859
6,862
6,863
6,863
2001
6,403
6,170
6,178
6,168
6,166
6,165
6,172
6,175
6,176
2002
5,404
5,391
5,378
5,385
5,392
5,407
5,406
5,406
2003
4,829
4,722
4,713
4,723
4,719
4,718
4,719
2004
4,198
4,138
4,098
4,109
4,110
4,109
2005
5,000
4,902
4,889
4,897
4,905
2006
6,026
6,022
6,038
6,050
2007
7,429
7,634
7,617
2008
8,609
9,006
2009
9,151
>
>
>
>
Growth in book?
Frequency deterioration?
Change in claim handling practices?
Change in report rate?
11
Diagnostics - Closed
Accident
Year
12
24
36
48
60
72
84
96
108
120
2000
2,236
5,005
5,891
6,311
6,549
6,646
6,704
6,748
6,787
6,792
2001
1,741
4,386
5,353
5,727
5,877
5,987
6,026
6,076
6,109
2002
1,275
3,838
4,704
5,023
5,169
5,252
5,297
5,347
2003
1,288
3,446
4,091
4,352
4,474
4,557
4,604
2004
1,003
2,712
3,486
3,736
3,877
3,978
2005
899
3,054
3,774
4,252
4,505
2006
970
3,150
4,717
5,282
2007
1,036
4,031
5,870
2008
1,253
4,676
2009
1,294
> Similar to reported
> Change in rate of settlement?
12
Diagnostics Closed to
Reported
Acciden
t Year
12
24
36
48
60
72
84
96
108
120
2000
0.316
0.726
0.856
0.920
0.954
0.968
0.977
0.983
0.989
0.990
2001
0.272
0.711
0.866
0.929
0.953
0.971
0.976
0.984
0.989
2002
0.236
0.712
0.875
0.933
0.959
0.971
0.980
0.989
2003
0.267
0.730
0.868
0.921
0.948
0.966
0.976
2004
0.239
0.655
0.851
0.909
0.943
0.968
2005
0.180
0.623
0.772
0.868
0.918
2006
0.161
0.523
0.781
0.873
2007
0.139
0.528
0.771
2008
0.146
0.519
2009
0.141
> Slow down in rate of settlement?
Regulatory change?
Volume or staffing?
Claim handling philosophy?
13
Diagnostics Average Paid
Accident
Year
12
24
36
48
60
72
84
96
108
120
2000
4,456
4,406
4,889
5,241
5,532
5,856
6,056
6,204
6,257
6,400
2001
5,150
4,745
4,966
5,354
5,581
5,720
6,024
6,216
6,629
2002
6,488
5,293
5,336
5,599
6,010
6,386
6,827
7,362
2003
6,798
4,862
5,065
5,447
6,018
6,660
7,050
2004
5,543
5,235
5,569
6,232
7,383
8,128
2005
8,075
6,259
7,159
7,832
8,666
2006
8,893
9,737
9,590
10,185
2007
13,808
11,145
10,568
2008
15,421
12,844
2009
20,119
> Rate of settlement?
Fast tracking of payments?
> Deterioration?
14
Diagnostics Average Case
Accident
Year
12
24
36
48
60
72
84
96
108
120
2000
10,613
14,039
19,990
27,631
38,501
45,153
63,241
79,559
114,743
121,801
2001
7,797
10,955
14,014
16,248
19,956
29,361
34,125
59,231
54,336
2002
6,853
9,077
11,809
17,773
23,643
45,206
49,591
45,792
2003
7,074
8,607
14,636
21,297
33,666
35,542
31,607
2004
7,153
9,526
16,736
30,472
36,382
36,200
2005
8,568
11,883
17,518
29,400
39,530
2006
8,745
11,846
17,059
28,257
2007
8,236
10,436
16,507
2008
8,209
9,583
2009
8,197
> Case reserves stable/strengthening/weakening?
> Keeping pace with average paid?
15
Development Techniques
16
Development to Ultimate
> Goal
Estimate ultimate losses for claims that
have already occurred
Fill in lower triangle!
> Requires significant judgment
Data accumulation
Techniques to use
Adjustments to Data
Remember diagnostics
Final selection
17
Development to Ultimate
> Hugh Whites Question
If actual losses are higher than expected
losses what do you do?
Assume future losses will be greater than
originally anticipated? (Development technique)
Assume future losses will be lower than originally
anticipated? (Expected Claims technique)
Assume future losses will be in line with original
estimate? (Bornhuetter-Ferguson technique)
18
Development Technique
> Development technique
aka Chain ladder Technique
> Assumptions
Future CY development similar to prior
AY losses to date provide relevant
information about the future of the AY
> Can be used on almost any type of data
19
Development Technique
1.
2.
3.
4.
5.
6.
Compile development triangle
Calculate age-to-age factors (LDFs)
Calculate average LDFs
Select LDFs
Select tail factor
Calculate cumulative claim development
factors (CDFs)
7. Project ultimate claims
20
Example Steps 1&2 (Paid)
Accident
Year
2002
2003
2004
2005
2006
2007
2008
2009
12
8,272
8,755
5,559
7,260
8,626
14,305
19,323
26,034
24
20,316
16,754
14,197
19,115
30,671
44,924
60,057
36
25,102
20,719
19,415
27,020
45,235
62,035
48
28,122
23,704
23,282
33,300
53,797
60
31,064
26,925
28,624
39,040
72
33,540
30,351
32,334
84
36,164
32,457
96
39,367
Accident
Year
2002
2003
2004
2005
2006
2007
2008
12-24
2.4559
1.9136
2.5537
2.6331
3.5556
3.1405
3.1080
24-36
1.2356
1.2367
1.3675
1.4135
1.4748
1.3809
36-48
1.1203
1.1441
1.1992
1.2324
1.1893
48-60
1.1046
1.1359
1.2294
1.1724
60-72
1.0797
1.1273
1.1296
72-84
1.0783
1.0694
84-96
1.0886
96-108
60,057
2008 12 24 =
19,323
21
Example Steps 3&4 (Paid)
Accident Year
2000
2001
2002
2003
2004
2005
2006
2007
2008
12-24
2.2134
2.3211
2.4559
1.9136
2.5537
2.6331
3.5556
3.1405
3.1080
24-36
1.3060
1.2773
1.2356
1.2367
1.3675
1.4135
1.4748
1.3809
36-48
1.1486
1.1535
1.1203
1.1441
1.1992
1.2324
1.1893
48-60
1.0953
1.0697
1.1046
1.1359
1.2294
1.1724
60-72
1.0742
1.0441
1.0797
1.1273
1.1296
72-84
1.0431
1.0601
1.0783
1.0694
84-96
1.0313
1.0403
1.0886
Averages
3 yr simple
3 yr medial
3 yr volume
3 yr geometric
3.2680
3.1405
3.2104
3.2619
1.4231
1.4135
1.4179
1.4225
1.2070
1.1992
1.2041
1.2068
1.1792
1.1724
1.1781
1.1786
1.1122
1.1273
1.1110
1.1120
1.0693
1.0694
1.0692
1.0692
1.0534
1.0403
1.0525
1.0531
Selected
3.2619
1.4225
1.2068
1.1786
1.1273
1.0692
1.055
22
Example Steps 3&4 (Paid)
> Common Averaging Techniques
Simple average
Medial average (exclude high/low)
Volume weighted average (aka dollar weighted)
Geometric average (
1/
=1 )
> Things to look for
Smooth progression
Stability within interval
Credibility
Applicability
23
Example Steps 5&6 (Paid)
> Tail factor selection will be discussed later
in the course
Accident Year
12
24
36
48
60
72
84
96
2002
8,272
20,316
25,102
28,122
31,064
33,540
36,164
39,367
2003
8,755
16,754
20,719
23,704
26,925
30,351
32,457
2004
5,559
14,197
19,415
23,282
28,624
32,334
2005
7,260
19,115
27,020
33,300
39,040
2006
8,626
30,671
45,235
53,797
2007
14,305
44,924
62,035
2008
19,323
60,057
2009
26,034
12-24
24-36
36-48
48-60
60-72
72-84
84-96
Selected
3.2619
1.4225
1.2068
1.1786
1.1273
1.0692
1.0550
CDF
8.3926
2.5730
1.8087
1.4987
1.2716
1.1280
1.0550
24
Example Step 7 (Paid)
12
24
36
48
60
72
84
96 (ULT)
Total
Reserve
2002
8,272
20,316
25,102
28,122
31,064
33,540
36,164
39,367
0
2003
8,755
16,754
20,719
23,704
26,925
30,351
32,457
34,242
1,785
2004
5,559
14,197
19,415
23,282
28,624
32,334
34,573
36,474
4,140
2005
7,260
19,115
27,020
33,300
39,040
44,008
47,055
49,643
10,603
2006
8,626
30,671
45,235
53,797
63,406
71,475
76,423
80,627
26,829
2007
14,305
44,924
62,035
74,867
88,239
99,468
106,354
112,204
50,168
2008
19,323
60,057
85,433
103,104
121,519
136,983
146,467
154,523
94,466
2009
26,034
84,918
120,799
145,785
171,824
193,690
207,100
218,490
192,456
12-24
24-36
36-48
48-60
60-72
72-84
84-96
Selected
3.2619
1.4225
1.2068
1.1786
1.1273
1.0692
1.0550
CDF
8.3926
2.5730
1.8087
1.4987
1.2716
1.1280
1.0550
Accident
Year
25
Development Technique
> When it doesnt work
Changing case adequacy (incurred)
Rate of settlement changes (paid)
Environmental changes
Insufficient data
Large losses
Low frequency high severity
Uneven distribution of claims
Highly leveraged (paid)
26
Expected Claims Technique
27
Expected Claims Technique
> Expected Claims Technique
aka Expected Loss Ratio Method
> Assumption
Experience to date doesnt better the a priori
estimate
> Typically used where there is a lack of
historical data
New line of business
New regulatory environment
Data is too immature
28
Expected Claims Technique
> Can be applied to any type of data
> Requires exposure base
Earned Premium (Auto and Property)
Policies in force (Auto and Property)
Total Insured Value (Property)
> Requires initial estimate of losses relative
to exposure base selected
Ult. Loss = Exposure x Loss Factor
eg. Earned Premium x Selected Loss Ratio
29
Example
Incurred
Earned Expected
Losses Premium Loss Ratio
Paid
Losses
2000
55,532
57,677
49,847
70%
34,893
-22,784
1,466
23,802
2001
71,685
75,751
53,645
70%
37,552
-38,199
1,414
26,557
2002
66,213
77,134
64,444
70%
45,111
-32,023
1,360
33,170
2003
56,374
68,890
86,504
70%
60,553
-8,337
1,274
47,530
2004
48,675
68,396
113,821
70%
79,675
11,279
1,260
63,235
2005
52,482
87,092
142,950
70%
100,065
12,973
1,276
78,440
2006
36,794
94,150
168,847
70%
118,193
24,042
1,546
76,428
2007
22,868
86,440
185,484
70%
129,839
43,399
1,428
90,919
2008
6,943
67,735
217,139
70%
151,998
84,262
1,377
110,382
2009
1,776
30,233
201,559
70%
141,091
110,858
1,514
93,191
Total
419,342
898,969
185,471
713,498 1,284,241
See exhibits 1-3
30
Ultimate
Incurred
Ultimate #
IBNR Claims x
CNP
Accident
Year
Average
Incurred
Expected Claims Technique
> How do we determine the loss ratio?
Industry data
Historical data
Other methods
Paid development
Incurred development
Judgment
31
Example
Accident Year
2000
2001
2002
2003
2004
2005
2006
2007
2008
2009
Total
Latest 8 AYs
Latest 7 AYs
Latest 6 AYs
Latest 5 AYs
Latest 4 AYs
Latest 3 AYs
Latest 2 AYs
Paid
Losses
55,532
71,685
66,213
56,374
48,675
52,482
36,794
22,868
6,943
1,776
419,342
Incurred
Paid LDFs
Losses
57,677
1.0215
75,751
1.0432
77,134
1.1014
68,890
1.1877
68,396
1.3944
87,092
1.7764
94,150
2.9486
86,440
5.9097
67,735
16.7590
30,233
67.5227
713,498
Incurred
LDFs
1.0000
1.0051
1.0063
1.0066
1.0178
1.0453
1.1228
1.3451
1.9255
3.2529
Weighted
Prior Avg Exl Latest
LR
70.3%
72.6%
63.7%
65.3%
61.2%
62.6%
61.3%
63.1%
60.5%
62.7%
59.6%
62.3%
55.5%
56.8%
Selected Loss Ratio
70%
32
Ultimate
Paid
56,726
74,783
72,926
66,955
67,873
93,231
108,492
135,141
116,358
119,952
912,437
Ultimate
Incurred
57,677
76,133
77,619
69,342
69,611
91,039
105,710
116,274
130,426
98,343
892,174
Selected
Ultimate
57,201
75,458
75,272
68,148
68,742
92,135
107,101
125,707
123,392
109,148
902,305
Earned
Loss Ratio
Premium
49,847
114.8%
53,645
140.7%
64,444
116.8%
86,504
78.8%
113,821
60.4%
142,950
64.5%
168,847
63.4%
185,484
67.8%
217,139
56.8%
201,559
54.2%
1,284,241
Example
Accident Year
2000
2001
2002
2003
2004
2005
2006
2007
2008
2009
Total
Paid Losses
55,532
71,685
66,213
56,374
48,675
52,482
36,794
22,868
6,943
1,776
419,342
Incurred Paid Development
Losses
IBNR
57,677
75,751
77,134
68,890
68,396
87,092
94,150
86,440
67,735
30,233
713,498
-952
-968
-4,208
-1,935
-522
6,139
14,342
48,701
48,622
89,719
198,939
What does this tell us???
33
Incurred
Expected Loss
Development
IBNR
IBNR
0
383
485
452
1,215
3,947
11,559
29,833
62,691
68,111
178,676
-22,784
-38,199
-32,023
-8,337
11,279
12,973
24,042
43,399
84,262
110,858
185,471
Expected Claims Technique
> Adjustments often required in selecting loss ratio
On-level
Loss trends
Reform Adjustment
> Advantages
Stability
Simplicity
Doesnt require too much data
> Disadvantages
Doesnt change unless assumptions change
Often requires significant judgment
34
Bornhuetter-Ferguson
Technique
35
Bornhuetter-Ferguson
Technique
> Blending of Development Technique and Expected
Claims Technique
> Assumptions
Unreported (not yet incurred) will develop based on expected
claims
Reported claims are credible
> Ultimate claims are split
Actual incurred to date
Expected unreported (not yet incurred)
> =
+
> =
%
36
Bornhuetter-Ferguson
Technique
1
% =
> Can be applied to any data
37
Example
Accident
Year
Paid Incurred
Losses Losses
Incurred
%
CDFs Unreported
Earned
Premium
Expected
Ultimate
Loss
Incurred
Ratio
Ultimate #
Average
IBNR Claims x
Incurred
CNP
2000
55,532
57,677
1.0000
0.00%
49,847
70%
57,677
0
1,466
39,343
2001
71,685
75,751
1.0051
0.50%
53,645
70%
75,939
189
1,414
53,705
2002
66,213
77,134
1.0063
0.63%
64,444
70%
77,416
282
1,360
56,923
2003
56,374
68,890
1.0066
0.65%
86,504
70%
69,284
394
1,274
54,383
2004
48,675
68,396
1.0178
1.75%
113,821
70%
69,786
1,391
1,260
55,387
2005
52,482
87,092
1.0453
4.34%
142,950
70%
91,430
4,338
1,276
71,671
2006
36,794
94,150
1.1228
10.93%
168,847
70%
107,075
12,924
1,546
69,239
2007
22,868
86,440
1.3451
25.66%
185,484
70%
119,754
33,314
1,428
83,857
2008
6,943
67,735
1.9255
48.07%
217,139
70%
140,795
73,059
1,377
102,246
2009
1,776
30,233
3.2529
69.26%
201,559
70%
127,950
97,717
1,514
84,511
Total
419,342
713,498
937,107
223,609
1,284,241
38
Bornhuetter-Ferguson
Technique
> Can be viewed as a credibility weighting of
the development method and expected
claims techniques
> Z = credibility factor
> =
1
> 0 1
> = + (1 )
39
Bornhuetter-Ferguson
Technique
> Advantages
Not distorted by random fluctuations in
immature data
Can be used with thin data
Can be used on short-tail and long-tail lines
> Disadvantage
Theoretical problem when development factors
are less than 1
Still heavily reliant on judgment
Should adjust historical data
40
Example
Paid
Incurred
Incurred
Development Development
Losses
IBNR
IBNR
Accident Year
Paid
Losses
2000
55,532
57,677
-952
0
-22,784
0
-1,411
2001
71,685
75,751
-968
383
-38,199
189
-2,510
2002
66,213
77,134
-4,208
485
-32,023
282
-6,768
2003
56,374
68,890
-1,935
452
-8,337
394
-2,947
2004
48,675
68,396
-522
1,215
11,279
1,391
2,816
2005
52,482
87,092
6,139
3,947
12,973
4,338
9,126
2006
36,794
94,150
14,342
11,559
24,042
12,924
20,752
2007
22,868
86,440
48,701
29,833
43,399
33,314
44,296
2008
6,943
67,735
48,622
62,691
84,262
73,059
82,135
2009
1,776
30,233
89,719
68,111
110,858
97,717
110,545
Total
419,342
713,498
198,939
178,676
185,471
223,609
256,035
41
Expected B-F Incurred
Loss IBNR
IBNR
B-F Paid
IBNR
Cape Cod Technique
42
Cape Cod Technique
> Cape Cod Technique
Aka Stanard-Buhlmann Method
> Very similar to B-F method
Only difference is the selection of the expected
loss ratio
> Loss ratio is derived not selected
Introduces concept of Used Up Premium
=
%
43
Example
Accident
Year
Paid Incurred
Losses Losses
Incurred
%
CDFs Unreported
Earned
Premium
Expected
Ultimate
Loss
Incurred
Ratio
Ultimate #
Average
IBNR Claims x
Incurred
CNP
2000
55,532
57,677
1.0000
0.00%
49,847
74%
57,677
0
1,466
39,343
2001
71,685
75,751
1.0051
0.50%
53,645
74%
75,950
199
1,414
53,713
2002
66,213
77,134
1.0063
0.63%
64,444
74%
77,432
298
1,360
56,935
2003
56,374
68,890
1.0066
0.65%
86,504
74%
69,307
417
1,274
54,401
2004
48,675
68,396
1.0178
1.75%
113,821
74%
69,865
1,469
1,260
55,449
2005
52,482
87,092
1.0453
4.34%
142,950
74%
91,675
4,583
1,276
71,863
2006
36,794
94,150
1.1228
10.93%
168,847
74%
107,805
13,654
1,546
69,711
2007
22,868
86,440
1.3451
25.66%
185,484
74%
121,636
35,195
1,428
85,175
2008
6,943
67,735
1.9255
48.07%
217,139
74%
144,921
77,185
1,377
105,242
2009
1,776
30,233
3.2529
69.26%
201,559
74%
133,468
103,235
1,514
88,156
Total
419,342
713,498
949,734
236,236
1,284,241
44
Example
Accident Year
Earned
Premium
Incurred
Incurred CDFs
Losses
% Reported
Used Up
Premium
Estimated
Loss Ratio
2000
49,847
57,677
1.0000
100.00%
49,847
115.7%
2001
53,645
75,751
1.0051
99.50%
53,375
141.9%
2002
64,444
77,134
1.0063
99.37%
64,041
120.4%
2003
86,504
68,890
1.0066
99.35%
85,940
80.2%
2004
113,821
68,396
1.0178
98.25%
111,834
61.2%
2005
142,950
87,092
1.0453
95.66%
136,753
63.7%
2006
168,847
94,150
1.1228
89.07%
150,383
62.6%
2007
185,484
86,440
1.3451
74.34%
137,893
62.7%
2008
217,139
67,735
1.9255
51.93%
112,769
60.1%
2009
201,559
30,233
3.2529
30.74%
61,963
48.8%
Total
1,284,241
713,498
964,800
74.0%
45
Cape Cod Technique
> Advantages
Not overly distorted by random fluctuations in immature
data
Judgment removed from B-F
Can be used on short-tail and long-tail lines
> Disadvantages
Theoretical problem when development factors are
less than 1
Judgment removed from B-F
Still heavily reliant on judgment
Should adjust historical data
46
Exercises
Incurred Losses
Accident Year
2005
2006
2007
2008
2009
12
1,500
1,650
1,815
1,997
2,196
24
3,000
3,630
4,356
4,792
36
4,500
5,082
6,970
48
4,635
5,336
2005
2006
2007
2008
2.0000
2.2000
2.4000
2.4000
1.5000
1.4000
1.6000
1.0300
1.0500
60
4,635
Earned
Premium
10,500
11,025
11,576
12,155
12,763
1.0000
Calculate the ultimate incurred loss based on the following:
Incurred development
Expected Loss Ratio
Bornhuetter-Ferguson
Cape Cod
47
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