Loss Triangle Philosophy
Gary Blumsohn
CARe Seminar:
Cambridge, May 2008
Background
Committee on Reinsurance Research
 Practical questions:

 Actuaries
mostly learn to do loss development
on the job
 Can we give guidance to improve approaches
– especially on unstable triangles?
The Questions
What types of averages do people use?
 Statistical tests and methods
 Smoothing
 Reversals
 Downward development
 Ignore tail-factor issue

Initial Attempt
12-year excerpt from RAA GL Fac
 Too stable!
 40 responses
 Mean loss reserve estimate = $1.6 billion
 SD of loss reserve estimates = $0.2 billion
CV = 13%

Second Attempt:
Umbrella incurred loss triangle
Accident
Year
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
1
1,782
430
2,234
3,335
2,006
7,640
6,643
2,474
4,229
2,065
3,448
1,736
2
3,000
2,814
3,902
12,937
5,406
8,485
13,184
9,684
6,135
2,982
4,240
3
6,924
3,557
10,841
23,694
9,802
12,085
18,530
10,636
5,972
3,384
4
10,167
5,745
14,262
20,477
8,949
13,515
17,782
16,266
8,613
5
12,369
9,033
17,666
19,715
10,611
15,418
20,867
16,649
6
14,047
7,884
19,154
23,689
10,623
18,894
21,358
7
13,577
8,715
19,411
23,955
16,633
19,029
8
14,289
8,982
19,021
25,066
16,699
9
13,831
9,048
18,854
25,269
10
14,419
8,934
19,085
11
14,563
8,856
2.308
1.264
2.778
1.831
1.813
1.424
1.405
1.098
0.973
1.135
1.468
1.615
1.316
0.864
0.913
1.118
0.960
1.529
1.442
1.217
1.572
1.239
0.963
1.186
1.141
1.173
1.024
1.136
0.873
1.084
1.202
1.001
1.225
1.024
0.967
1.105
1.013
1.011
1.566
1.007
1.052
1.031
0.980
1.046
1.004
0.968
1.007
0.991
1.008
1.043
0.987
1.012
1.010
0.991
0.995
Age-to-age
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
1.684
6.544
1.747
3.879
2.695
1.111
1.985
3.914
1.451
1.444
1.230
12
14,484
Responses

“Great and gutsy project!”

“I believe the whole notion of "picking
factors" with no statistical guidance is
something of a disgrace to the
profession…”
Responses (cont.)

“While it may be helpful to share ideas on how to pick
LDFs, it is vital that more information than just the
triangle at hand be considered… I wouldn’t make
selections without other information such as individual
claim information, changes in the underlying business,
comparison to competitor or industry triangles if
available, etc. Of course you can’t always get the
information you want……but I would hate to see people
come to the seminar and learn some new selection
techniques that don’t look beyond the triangle.”
ATA factors
3.0
2.8
2.6
2.4
2.2
2.0
1.8
1.6
1.4
1.2
1.0
0.8 0
51 responses
2
4
6
Development age
8
10
ATU factors
12.0
10.0
8.0
6.0
4.0
2.0
0.0
0
2
4
6
Development Age
8
10
# of responses
Frequency of Reserves
17
15
13
11
9
7
5
3
1
-1
Implied Reserves
(in
$millions)
13
18
23
28
33
38
43
48
53
58
Projected loss reserve ($millions)
Percentile
Cumulative Distribution of Loss Reserves
100%
90%
80%
70%
60%
50%
40%
30%
20%
10%
0%
Mean
-
20
40
Loss Reserves ($millions)
60
Mean
28.0
Std. Dev
8.3
Minimum
10.7
2nd lowest
18.3
25th percentile
23.7
Median
26.2
75th percentile
31.1
2nd highest
55.2
Maximum
60.2
Loss Reserves (in $millions)
Mean Loss Reserve
Rptd to date
High
Low
Median
30
25
20
15
10
5
0
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
“Actuaries must not pretend to judge
what they cannot scientifically model.”
Leigh Halliwell
Variance, Vol. 1, Issue 2, p. 216
Skeptic’s view of statistical
methods

Statistical methods measure the past

You have how many data points?!!

Blow-ups more likely to be from things that
aren’t in the data than from 1-in-10,000
events.
Task Force On The Reputation Of Casualty
Actuaries
Economic Perspective
Complete determinism:
Know the future
Perfect
Knowledge
Stochastic determinism:
Know the future statistically
Risk
No determinism:
Don’t know distributions
Uncertainty
Blumsohn, PCAS 1999, p. 31
“If you cannot measure,
your knowledge is meager
and unsatisfactory.”
Lord Kelvin
The Dilemma
Your knowledge is meager and
unsatisfactory,
but your boss needs an answer
Frank Knight, on the practical meaning of
Kelvin’s statement for social scientists:
“If you cannot measure,
measure anyhow.”