Claims Reserving for Non Life
Insurance
Craig Thorburn, B.Ec., F.I.A.A.
Cthorburn@worldbank.org
Phone +1 202 473 4932
Agenda
•
•
•
•
The objectives of loss reserving
Techniques
The role of the supervisor
Illustrative examples
Objectives of Loss Reserving
• The statistical basis of insurance
• Supervisory objectives
• Company objectives
The Statistical Basis of Insurance
The Ultimate Cost of an Insurance Risk
Distribution of possible
numbers of events
occurring during the
period of exposure
Distribution of possible
Costs arising from an
event occurring during
the period of exposure
Possible number of events
Probability Distribution
Amount of Payment
Distribution
Timing of Payment
Distribution
The Risk of Ruin
• Taking account of
–
–
–
–
Expected and unexpected events
Expected and unexpected outcomes of size of claims
Expected and unexpected timing issues
The potential for misestimating values
• What is the chance that we will not have enough
funds to meet our obligations?
• Do we have enough resources to cover the
potential adversity in outcome?
At an acceptably small
probability of being wrong
Point where
claims use
up available
resources
Total Claims Cost
Probability of
Exceeding
“Ruin”
Supervisory Objectives
• Adequacy
• Normally, assessment on a “not less than
reasonable” basis
• Value relates to determining excess assets
• Value can relate to determining solvency
margin requirements
Company Objectives
• Economic capital requirements
• Other external pressures
– Ratings agencies
– Solvency breach minimisation
• Profit smoothing
• Taxation management
• Management remuneration schemes
Small Numbers and Large
Numbers
• On the balance sheet numbers are small
• On the P&L numbers are large
• For example
–
–
–
–
Company seeks profit of 3% of premiums
Investment earnings are 10% pa
Business is long tail (term 4 years)
2% increase in provisioning will eliminate the
year’s profit
Agenda
•
•
•
•
The objectives of loss reserving
Techniques
The role of the supervisor
Illustrative examples
Techniques
•
•
•
•
•
Case estimates
Run-off methods
Stochastic methods
Advantages and disadvantages
Issues
– Establishing assumptions
– Reinsurance allowance
– Quality of data
Case Estimates
• Each claim has a file opened when it is
notified
• Estimates are made, and updated, as
information comes to hand
• Payments made are recorded against the file
• When the claim is finalised, the file is
closed
Run-off Methods
• Use models to complete the future expected
payments
• Several methods are available
• Assume past (observed) processes continue
into the future
Stochastic Methods
• Full models of claims size and delay are
established
• Can be enhanced by simulation methods
• Provide a great deal of information about
the range of answers – not just one answer
Advantages and Disadvantages
• Case estimates do not include IBNR
• Case estimates use all available information about
a claim
• Case estimates can be biased by management
attitudes
• Case estimates are easy to implement
• Run-off and Stochastic methods rely on stability
of procedures and quality of data
• Run-off and Stochastic methods are more difficult
to implement and to interpret
Issues
• Establishing Assumptions
• Reinsurance allowance
• Quality of data
Questions and
comments
Agenda
•
•
•
•
The objectives of loss reserving
Techniques
The role of the supervisor
Illustrative Examples
The role of the supervisor
• What can you do?
–
–
–
–
–
Ratio analysis
Runoff methods
Back-testing Case Estimates
Use of Actuaries
On Site Inspections
Ratio Analysis
• Collect data on the numbers of claims, case
estimates, and amounts of claims to date
and expected by business line and accident
year.
• Compare company to company and period
to period looking for extremes and sudden
changes.
Runoff Methods
• Can be applied to data submitted to check
answers for reasonableness
• Ideally, several methods would be used
Back-testing Case Estimates
• Important to see how adequate they have
been.
• Compare last year’s case estimates with this
year plus claims paid less allowance for
investment income and expenses.
• Similar to case estimate development
method (covered later).
Use of Actuaries
• Interview actuaries who have done
evaluations.
• Read existing actuarial reports.
• Compare actuarial methods and
assumptions.
• Seek an independent actuarial report.
• Employ internal actuaries in the supervisor.
On Site Inspections
• Activity will depend on time taken and
assessed risk
– Examine actuarial data sources
– Examine actuarial processes
– Review assumptions
Agenda
•
•
•
•
The objectives of loss reserving
Techniques
The role of the supervisor
Illustrative example
Illustrations
• Chain ladder method
– Based on CUMULATIVE data
– Can do numbers or amounts of claims incurred
or paid or case estimates
The Starting Point
Accident Year
1995
1996
1997
1998
1999
2000
2001
Development Year
1
2
776
892
1141
882
1583
2374
4375
200
178
257
242
416
526
3
4
5
6
7
54
71
72
63
107
20
24
30
27
4
7
9
3
5
0
Historic data
Past numbers of claims for each year
Accident Year
1995
1996
1997
1998
1999
2000
2001
Development Year
1
2
776
892
1141
882
1583
2374
4375
200
178
257
242
416
526
3
4
5
6
7
54
71
72
63
107
20
24
30
27
4
7
9
3
5
0
• It is important to have quality data which is homogeneous
• Separate business lines and categories
The Objective
Past numbers of claims for each year
Accident Year
1995
1996
1997
1998
1999
2000
2001
Development Year
1
2
776
892
1141
882
1583
2374
4375
200
178
257
242
416
526
3
4
5
6
7
54
71
72
63
107
20
24
30
27
4
7
9
3
5
0
Filling in the gap…
Step 1: Make the Table
Cumulative
Accident Year
1995
1996
1997
1998
1999
2000
2001
Development Year
1
2
776
892
1141
882
1583
2374
4375
976
1070
1398
1124
1999
2900
3
4
5
6
7
1030
1141
1470
1187
2106
1050
1165
1500
1214
1054
1172
1509
1057
1177
1057
Step 2: Calculate Ratios
Accident Year
1995
1996
1997
1998
1999
2000
2001
Average
Weighted Average
1
2
3
4
5
6
7
1.2577
1.1996
1.2252
1.2744
1.2628
1.2216
1.0553
1.0664
1.0515
1.0560
1.0535
1.0194
1.0210
1.0204
1.0227
1.0038
1.0060
1.0060
1.0028
1.0043
1.0000
1.2402
1.2378
1.0566
1.0559
1.0209
1.0209
1.0053
1.0054
1.0036
1.0036
1.0000
1.0000
Step 3: Apply Ratios to Project
Figures
Ratios Applied
Accident Year
1995
1996
1997
1998
1999
2000
2001
Development Year
1
2
776
892
1141
882
1583
2374
4375
976
1070
1398
1124
1999
2900
5415
3
4
5
6
7
1030
1141
1470
1187
2106
3062
5717
1050
1165
1500
1214
2150
3126
5836
1054
1172
1509
1220
2161
3142
5867
1057
1177
1514
1224
2168
3153
5888
1057
1177
1514
1224
2168
3153
5888
Actual Data I used…
Accident Year
1995
1996
1997
1998
1999
2000
2001
Development Year
1
2
776
892
1141
882
1583
2374
4375
200
178
257
242
416
526
970
3
4
5
6
7
54
71
72
63
107
161
274
20
24
30
27
44
72
92
4
7
9
7
10
17
27
3
5
5
5
8
13
22
0
0
0
0
0
0
0
Comparison of Results
Accident Year
1995
1996
1997
1998
1999
2000
2001
Total
Claims
Total
Reported Projected
so far
Claims
Total
Actual
Claims
Future
Claims
Modelled
Future
Actual
Claims Difference
1057
1177
1509
1214
2106
2900
4375
1057
1177
1514
1224
2168
3153
5888
1057
1177
1514
1226
2168
3163
5760
0
0
5
10
62
253
1513
0
0
5
12
62
263
1385
0
0
0
2
0
10
-128
14338
16181
16065
1843
1727
-116
Number of Observations
150 cases using average ratio
Sample Distribution of Results
35
30
25
20
15
10
5
0
-257.5
-180
-102.5
-25
52.5
130
207.5
285
362.5
440
-335
-257.5
-180
-102.5
-25
52.5
130
207.5
285
362.5
Range
• 45% proved, in hindsight, to be adequate
Number of Observations
150 cases using worst observed
ratio
Sample Distribution of Results
40
35
30
25
20
15
10
5
0
-627.2
-517.4
-407.6
-297.8
-188
-78.2
31.6
141.4
251.2
361
-737
-627.2
-517.4
-407.6
-297.8
-188
-78.2
31.6
141.4
251.2
Range
• 92% proved, in hindsight, to be adequate
Questions and
comments