Transcript Predictive Modeling in Reserving

IMPROVING ACTUARIAL RESERVE
ANALYSIS THROUGH CLAIM-LEVEL
PREDICTIVE ANALYTICS
Presenter: Chris Gross
1
Predictive Modeling in Reserve
Analysis
• It’s all predictive modeling isn’t it?
• This discussion refers to the what is commonly
termed ‘predictive modeling’- multivariate
models, statistical rigor, etc.
• Emphasis in the past on pricing
• Reserving getting attention
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Case Reserve Adequacy Example
Calendar
Period
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
Combined
Open
Case
Count
Reserves
564
4,954,014
568
6,198,630
649
5,347,576
674
6,067,343
543
5,313,733
590
5,666,509
631
6,927,816
731
7,125,765
590
6,493,882
697
7,773,533
660
7,021,701
678
5,778,941
528
5,795,591
541
5,268,996
941
7,110,736
823
6,631,955
707
5,615,405
842
7,115,139
954
7,139,176
12,911 119,346,440
Average
Case
Reserve
8,784
10,913
8,240
9,002
9,786
9,604
10,979
9,748
11,007
11,153
10,639
8,524
10,976
9,739
7,557
8,058
7,943
8,450
7,483
9,244
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Case Reserve Adequacy Example
Accident Period
Average Case
Reserves
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
Age
1
7,105
7,425
5,418
6,023
6,667
5,647
9,031
7,333
8,290
8,292
5,733
6,172
7,964
5,695
5,086
5,595
6,293
5,207
4,605
2
8,083
8,079
9,161
7,361
7,660
11,333
8,594
8,283
12,039
15,097
14,563
7,960
8,008
10,467
7,318
7,900
7,308
9,071
7,730
3
13,606
11,215
10,475
8,555
14,058
12,017
12,659
10,021
12,626
8,452
11,663
12,252
8,312
8,994
13,008
9,937
9,373
8,055
7,172
4
11,331
17,543
7,118
11,119
15,436
13,784
13,242
11,197
23,137
12,802
30,860
12,336
31,963
14,460
17,823
8,360
14,810
15,745
11,351
5
6,030
18,579
12,071
9,795
12,694
6,572
15,392
22,099
7,531
15,536
17,409
12,491
19,280
15,778
8,781
17,125
10,024
19,155
23,693
6
30,457
32,481
20,569
17,182
13,921
24,061
15,662
6,633
11,470
18,592
11,719
33,697
32,925
14,183
15,291
20,298
17,383
19,829
12,661
7
13,168
57,601
64,389
29,027
12,122
7,462
17,083
24,329
10,383
12,114
2,718
12,401
7,833
27,371
50,042
15,324
7,253
17,468
20,106
8
512
43,387
34,507
53
17,082
13,483
7,789
11,479
13,195
18,718
14,543
20,921
4,044
35,736
13,483
37,290
14,548
7,433
8,057
9
10
118
74,052
255
16,540
18,534
6,464
7,013
19,990
21,325
4,401
13,429
7,681
11,894
18,818
14,578
15,318
15,853
4,486
30,793
24,697
22,693
13,056
8,385
17,439
24,451
4,504
6,422
7,004
55
13,454
16,353
40,260
15,589
11
548
467
12,588
8,981
32,308
9,569
16,903
12,778
1,223
12,790
23,625
21,444
33,349
4,599
34,826
3,416
12
57,087
13,320
19,056
19,703
17,854
10,769
6,925
7,906
23,073
11,855
9,392
344
14,686
9,822
19,515
13
14
15
16
11,290
3,207
19,144
10,363
9,117
4,454
12,905
11,437
17,316
16,623
6,983
54,026
29,958
458
1,744
2
24,879
14,123
11,053
11,363
4,161
53,291
1,797
798
3,709
1,041
5,859
5,517
3,569
7,801
28,212
5,285
3,073
22,349
22,333
17,284
15,746
1,318
3,422
5,810
11,400
14,575
24,411
20,446
17
18
19
4,483
146
6,580 10,847
334 168,510
1,248
8,134
24,711
12,421
10,715
14,796
2,013
56,507
37,824
20
21
9
6,939
3,371
4
Case Reserve Adequacy Example
16,000
Average Case Reserve
14,000
12,000
Age 3
10,000
Age 2
8,000
Age 1
6,000
4,000
1
3
5
7
9 11 13 15 17 19 21 23
Calendar Period
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Case Reserve Adequacy Example
• Mix issues
–
–
–
–
Different classes of business
Different causes of loss
Geography
Etc.
• Can generate average case reserve triangles at each
of these levels but reduced volume of
data/increased volume of triangles can make the
situation more difficult to see.
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Case Reserve Adequacy Example
Same calendar
period data, but
include
credibility (in
this case based
on rank based tstatistic of
observations)
and smoothing
techniques.
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Case Reserve Adequacy Example
At the very least,
the inclusion of Age
of Development is
appropriate in a
predictive model of
case reserves
In this case it is very
predictive
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Case Reserve Adequacy Example
Not surprisingly,
the age of
development
has a strong
impact on the
size of the case
reserve.
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Case Reserve Adequacy Example
The calendar
period, when
adjusted for age
of development
(orange dots)
now shows a
more muted
impact on case
reserves, but
still cause for
concern.
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Case Reserve Adequacy Example
Addition of
other variables
is easy–
particularly
those that are
already on the
claim record.
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Case Reserve Adequacy Example
The policy form
was also
predictive.
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Case Reserve Adequacy Example
Our primary
question
remains. Is there
a change by
calendar period?
After adjusting
for the other
variables, there
is much less
evidence of a
change in
adequacy over
time.
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Case Reserve Adequacy Example
A lift chart for
the model that
uses Calendar
Period alone.
Calendar Period
by itself, does
little to describe
the size of the
case reserve in
this example.
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Case Reserve Adequacy Example
A lift chart using
Calendar Period
and Age of
Development.
This model does
a considerably
better job of
describing case
reserve size.
(Hence our use
of average case
triangles)
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Case Reserve Adequacy Example
This lift chart
includes the impact
of other variables.
Adding variables like
cause of loss results
in a much better
model of case
reserves.
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Case Reserve Adequacy Example
This lift chart shows
a model where the
other variables are
left in, and calendar
period is removed.
The impact of
calendar period is
relatively
insignificant, after
normalizing for the
impact of other
variables.
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Case Reserve Adequacy Example
• Consider the following scenario:
– Pressure on underwriting to write tougher, more severe
classes.
– Pressure on claim department to be more aggressive on
setting case reserves.
– What would this combination look like in terms of average
case reserve?
– Could very well be flat. Normal diagnostics may miss it.
– Predictive modeling could help alert the actuary to this
situation.
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Ways to Incorporate Predictive
Modeling Into Reserve Analysis
• Analysis of specific loss development
data/processes, for example:
– Case reserve adequacy
– Closure rates
• Modification of triangles
• Reserve segmentation
• Full description of the entire process, with
resulting estimate of reserves
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Why do it?
• Use more of the information contained in your
data
• Improve predictive accuracy
• Quicker recognition of changing environment
• Better reserve allocations
• Layering of losses
• Improved operational or strategic business
decisions
20
Challenges
• Same as with P&C reserving in general
– Loss development occurs over time, mature
periods are old
– Immature claims contain information
• Many facets of loss development
• Helpful to concentrate on a single time-step
(e.g. beginning of quarter to end of quarter)
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Data
Financial Data
Beginning Case Reserve
Ending Case Reserve
Payment in Period
Exposure Characteristics
Type
Product
ZIP Code
Timing Data
Accident Quarter
Report Quarter
Valuation Quarter
Claim Characteristics
Loss Cause
Loss Cause - Detail
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Claim activity from the beginning of
the quarter to the end of the quarter
Does the
Claim Have a
New Value?
What is the
New Value?
Did the Claim
Close?
Is there a
Payment?
How much is
the Payment?
Arrows indicate dependency on other results
A number of available claim or exposure characteristics may have predictive
value for any of these questions.
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Probability of a Claim Closing
• Base probability of
71%
• Modification of this
probability by various
claim characteristic
values that were
found to have
predictive value
24
Close Probability – Claim Age
25
Close Probability – Loss Cause
(detailed)
26
Close Probability – Loss Cause
27
Close Probability – Accident Quarter
28
Close Probability - Product
29
Close Probability - Type
30
Probability of Change in Value (Given
Not Closed)
• Base probability of
37%
• 4 characteristics
found to be
predictive
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Change Probability – Claim Age
32
Change Probability – Loss Cause
33
New Claim Value (Given Changed but
Not Closed)
• Base factor of 1.98 to
beginning case
reserve
• Modification to this
linear relationship, as
well as five additional
predictive
characteristics
34
New Claim Value - Case Reserve
35
New Claim Value – Loss Cause
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1.6 - 1.7
1.5 - 1.6
1.4 - 1.5
1.3 - 1.4
1.2 - 1.3
1.1 - 1.2
1.0 - 1.1
0.9 - 1.0
0.8 - 0.9
0.7 - 0.8
0.6 - 0.7
Number of ZIP Codes
New Claim Value – ZIP Code
100
90
80
70
60
50
40
30
20
10
0
Factor
37
New Claim Value- Loss Cause (Detail)
38
New Claim Value - Product
39
Bringing it together
• Simulation can be used to project activity in
the next quarter
• It is necessary to project not only the
predictive relationships, but also the residual
error term.
• Chain through quarters using information
from the previous simulated quarter.
• Store results, preferably at the claim level.
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Simulate Going Forward
• Claim Development
– Start with current inventory of open claims
– For each open claim simulate a number of
potential outcomes for the next time-step (using
the claims’ characteristics)
– For those simulated claim-paths that are still open
simulate forward another time-step.
– Continue until all simulated claim-paths are closed
Claim 1
Claim 2
Claim 3
Simulated Future Development (Mean Path)
8,000,000
7,000,000
6,000,000
5,000,000
4,000,000
Case
3,000,000
Paid
2,000,000
1,000,000
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Future Quarter
45
14,000,000
Grand Total
12,000,000
10,000,000
8,000,000
6,000,000
4,000,000
Probability distribution of total
payments
2,000,000
0
0.2
0.4
0.6
0.8
1
46
14,000,000
Grand Total
12,000,000
10,000,000
Mean of total payments
8,000,000
6,000,000
4,000,000
2,000,000
0
0.2
0.4
0.6
0.8
1
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14,000,000
Grand Total
12,000,000
10,000,000
8,000,000
6,000,000
4,000,000
Current case reserves
2,000,000
0
0.2
0.4
0.6
0.8
1
48
12,000,000
6,000,000
Product 1
10,000,000
Product 2
5,000,000
8,000,000
4,000,000
6,000,000
3,000,000
4,000,000
2,000,000
2,000,000
1,000,000
-
0
0.2
0.4
0.6
0.8
1
400,000
0
0.2
0.4
0.6
0.8
1
0.4
0.6
0.8
1
2,500,000
Product 3
350,000
Product 4
2,000,000
300,000
250,000
1,500,000
200,000
1,000,000
150,000
100,000
500,000
50,000
-
0
0.2
0.4
0.6
0.8
1
0
0.2
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10,000,000
1,600,000
9,000,000
Type 1
1,400,000
Type 2
8,000,000
1,200,000
7,000,000
1,000,000
6,000,000
800,000
5,000,000
4,000,000
600,000
3,000,000
400,000
2,000,000
200,000
1,000,000
-
0
0.2
0.4
0.6
0.8
1
0.4
0.6
0.8
1
0
0.2
0.4
0.6
0.8
1
9,000,000
8,000,000
Type 3
7,000,000
6,000,000
5,000,000
4,000,000
3,000,000
2,000,000
1,000,000
0
0.2
50
4,500,000
1,400,000
4,000,000
Loss Cause 1
Loss Cause 2
1,200,000
3,500,000
1,000,000
3,000,000
2,500,000
800,000
2,000,000
600,000
1,500,000
400,000
1,000,000
200,000
500,000
-
0
0.2
0.4
0.6
0.8
1
800,000
0
0.2
0.4
0.6
0.8
1
0.6
0.8
1
0.6
0.8
1
10,000,000
9,000,000
Loss Cause 3
700,000
Loss Cause 4
8,000,000
600,000
7,000,000
500,000
6,000,000
400,000
5,000,000
300,000
4,000,000
3,000,000
200,000
2,000,000
100,000
1,000,000
-
0
0.2
0.4
0.6
0.8
1
900,000
0
0.2
0.4
2,500,000
800,000
Loss Cause 5
Loss Cause 6
2,000,000
700,000
600,000
1,500,000
500,000
400,000
1,000,000
300,000
200,000
500,000
100,000
-
0
0.2
0.4
0.6
0.8
1
0
0.2
0.4
51
Emergence
• After simulating claim development to
ultimate, model emergence
• Frequency
• Severity
• Report Lag
52
Claim Emergence
Claim
Development
Simulation
Ultimate
Claim Severity
Report Lag
Claim
Frequency
Arrows indicate dependency on other results
A number of exposure characteristics may have predictive value for any of
these questions.
53
Emergence Simulation
• Use written policies (w/ characteristics)
simulate remaining emergence.
• Generating loss date within this process allows
accident period calculations
• Also get losses associated with unearned
premium
• Inforce loss ratio distribution.
Discussion of Additional Complexity
•
•
•
•
Relationship between Loss and ALAE
Re-opened claims
Changing claim characteristics
Salvage & Subrogation
55
Uses
•
•
•
•
•
•
Claim management
Reserve Analysis
Pricing Analysis
Underwriting Management
Risk Management
Reinsurance