claims reserving for non life insurance craig thorburn, b.ec., f.i.a.a. [email protected]...
TRANSCRIPT
Claims Reserving for Non Life Insurance
Craig Thorburn, B.Ec., F.I.A.A.
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 possiblenumbers of events
occurring during theperiod of exposure
Possible number of events
Probability Distribution
Distribution of possibleCosts arising from an
event occurring duringthe period of exposure
Amount of PaymentDistribution
Timing of PaymentDistribution
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
Total Claims Cost
Point where claims use up available resources
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
Development YearAccident Year 1 2 3 4 5 6 7
1995 776 200 54 20 4 3 01996 892 178 71 24 7 51997 1141 257 72 30 91998 882 242 63 271999 1583 416 1072000 2374 5262001 4375
Development YearAccident Year 1 2 3 4 5 6 7
1995 776 200 54 20 4 3 01996 892 178 71 24 7 51997 1141 257 72 30 91998 882 242 63 271999 1583 416 1072000 2374 5262001 4375
Historic data
Past numbers of claims for each year
• It is important to have quality data which is homogeneous
• Separate business lines and categories
Development YearAccident Year 1 2 3 4 5 6 7
1995 776 200 54 20 4 3 01996 892 178 71 24 7 51997 1141 257 72 30 91998 882 242 63 271999 1583 416 1072000 2374 5262001 4375
The Objective
Past numbers of claims for each year
Filling in the gap…
Step 1: Make the Table Cumulative
Development YearAccident Year 1 2 3 4 5 6 7
1995 776 976 1030 1050 1054 1057 10571996 892 1070 1141 1165 1172 11771997 1141 1398 1470 1500 15091998 882 1124 1187 12141999 1583 1999 21062000 2374 29002001 4375
Step 2: Calculate Ratios
Accident Year 1 2 3 4 5 6 7
1995 1.2577 1.0553 1.0194 1.0038 1.0028 1.0000 1996 1.1996 1.0664 1.0210 1.0060 1.0043 1997 1.2252 1.0515 1.0204 1.0060 1998 1.2744 1.0560 1.0227 1999 1.2628 1.0535 2000 1.2216 2001
Average 1.2402 1.0566 1.0209 1.0053 1.0036 1.0000 Weighted Average 1.2378 1.0559 1.0209 1.0054 1.0036 1.0000
Step 3: Apply Ratios to Project Figures
Ratios Applied Development YearAccident Year 1 2 3 4 5 6 7
1995 776 976 1030 1050 1054 1057 10571996 892 1070 1141 1165 1172 1177 11771997 1141 1398 1470 1500 1509 1514 15141998 882 1124 1187 1214 1220 1224 12241999 1583 1999 2106 2150 2161 2168 21682000 2374 2900 3062 3126 3142 3153 31532001 4375 5415 5717 5836 5867 5888 5888
Actual Data I used…
Development YearAccident Year 1 2 3 4 5 6 7
1995 776 200 54 20 4 3 01996 892 178 71 24 7 5 01997 1141 257 72 30 9 5 01998 882 242 63 27 7 5 01999 1583 416 107 44 10 8 02000 2374 526 161 72 17 13 02001 4375 970 274 92 27 22 0
Comparison of Results
Accident Year
Claims Reported
so far
Total Projected
Claims
Total Actual
Claims
Future Claims
Modelled
Future Actual
Claims Difference
1995 1057 1057 1057 0 0 01996 1177 1177 1177 0 0 01997 1509 1514 1514 5 5 01998 1214 1224 1226 10 12 21999 2106 2168 2168 62 62 02000 2900 3153 3163 253 263 102001 4375 5888 5760 1513 1385 -128
Total 14338 16181 16065 1843 1727 -116
150 cases using average ratio
Sample Distribution of Results
0
5
10
15
20
25
30
35
-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
Nu
mb
er
of
Ob
se
rva
tio
ns
• 45% proved, in hindsight, to be adequate
150 cases using worst observed ratio
Sample Distribution of Results
0
5
10
15
20
25
30
35
40
-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
Nu
mb
er
of
Ob
se
rva
tio
ns
• 92% proved, in hindsight, to be adequate
Questions and comments
