Transcript Document

METODOLOGÍAS Y PRÁCTICAS
EN RESERVAS TÉCNICAS
PARA SEGUROS DE SALUD
Y SEGUROS GENERALES
■ Advantages and Limitations ■
LIMA - 31 DE MAYO, 2007
APESEG
Presentado por: APESEG & Milliman, Inc.
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RESERVING METHODS IN PRACTICE
UK Survey - Projection Methods used in Practice
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
Chain ladder
Bornhuetter-Ferguson
Loss Ratio x Premiums
Average Cost Per Claim
Exposure-based method
Inflation Adjusted Average Cost Per Claim
IBNR to Case Reserve Ratio
Inflation-adjusted chain ladder
Regularly
Less frequently
Source: Claims Reserving Working Party Paper
Once in a blue moon
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EXPLORATORY DATA ANALYSIS
 Rate of Development
 Smoothness of Development
 Presence (absence) of Large Losses
 Volume of Data
3
EXPLORATORY DATA ANALYSIS
 Appropriate Projection Methodologies
 Anomalies in the data
 Questions to ask management concerning issues
manifested in the data
4
ANALYST RESPONSIBILITIES
 Recognize normal levels of random fluctuation
 Recognize aberrations in loss development patterns
 Recognize trends in loss development patterns
 Question management concerning patterns
 Identify underlying causes of aberrations
 Make adjustments/corrections as necessary
5
SENSITIVITY TESTS
 Optimistic/Pessimistic Loss Development Factor
Selections
 Optimistic/Pessimistic Tail Factor Selections
 Optimistic/Pessimistic Bornhuetter-Ferguson
Expected Loss Estimates (Loss Ratios)
 Different Weighting among methods
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WHEN THINGS GO WRONG
 Management reviews the prior year actuarial report
and fires claims manager because case reserves
develop upwards over time
 New claims manager instructs staff to reserve all
claims at probable maximum amount
 This results in an average 10% increase in the
average outstanding reserve along the last diagonal
 What will happen to the incurred loss development
method?
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COMPARISON BEFORE AND AFTER
STRENGTHENING
Accident Cumulative
Year
Paid
2000
78,224
2001
81,287
2002
66,402
2003
62,347
2004
62,832
2005
33,568
2006
11,346
Total
Ultimate
Reserve
Ultimate
Difference
Before
Before
After
as Percent
Strengthening Strengthening Strengthing Difference of Reserve
82,372
4,148
82,787
415
10%
87,511
6,224
88,568
1,057
17%
70,499
4,097
71,469
969
24%
80,394
18,047
82,841
2,447
14%
92,156
29,324
96,247
4,091
14%
64,040
30,472
68,134
4,094
13%
44,467
33,121
48,495
4,028
12%
125,433
17,101
14%
Case Reserve Strengthening had a
leveraged impact on the reserve –
Reserves overstated by 14%
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WHEN THINGS GO WRONG
 Management pushes claims department to settle
more claims
 In 2006, claims department settled an additional
10% of claims (at the average outstanding + IBNR
reserve)
 What will happen to the paid loss development
method?
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COMPARISON BEFORE AND AFTER
ACCELERATION
Ultimate
Accident Cumulative
Before
Year
Paid
Acceleration
2000
78,459
80,571
2001
81,782
86,232
2002
67,183
74,210
2003
63,771
76,582
2004
65,846
92,968
2005
36,982
67,706
2006
14,676
44,643
Total
Reserve
Ultimate
Difference
Before
After
as Percent
Acceleration Acceleration Difference of Reserve
2,112
80,812
242
11%
4,451
87,017
785
18%
7,027
75,534
1,324
19%
12,812
79,111
2,529
20%
27,122
98,974
6,006
22%
30,724
76,556
8,851
29%
29,967
60,282
15,640
52%
114,215
35,376
31%
Settlement acceleration had a
leveraged impact on the reserve –
Reserves overstated by 31%!
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LOSS RATIO
 Implicit Assumption
─ Loss Ratio is known or can be reasonably estimated
─ Ultimate Loss is proportional to exposures (premium)
 Strengths
─ Simplicity
─ Basic data requirements
─ Can use Pricing Assumptions concerning Loss Ratio
 Weaknesses
─ Depends entirely on quality of Loss Ratio estimate
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PAID LOSS DEVELOPMENT
 Implicit Assumption
─ Losses are paid at the same rate regardless of
accident year
 Strengths
─ Simplicity
─ Basic data requirements
─ Does not depend upon case reserves
─ Provides objective test of incurred loss development
 Weaknesses
─ Sensitive to changes in rate of settlement
─ Results for immature year may be erratic
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INCURRED LOSS DEVELOPMENT
 Implicit Assumption
─ Strength of case reserves is dependent only on the
delay from accident date
 Strengths
─ Simplicity
─ Basic data requirements
─ Converges to ultimate faster than paid method
─ May be better than paid for immature years
 Weaknesses
─ Sensitive to changes in case reserve adequacy
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BORNHUETTER-FERGUSON
 Implicit Assumption
─ Reserve is dependent upon the loss ratio, exposures,
and development pattern
 Strengths
─ Combines loss ratio method with development
method
─ Avoids problem with development method instability
for immature years
─ Good to use when data are erratic
 Weaknesses
─ Dependent on the quality of the loss ratio
─ Requires data on exposures as well as triangle data
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STRENGTHS / WEAKNESSES
Strengths
 Methods are intuitive –
once data is arranged in
triangle patterns become
obvious
 No sophisticated
mathematics involved
 Spreadsheets can be
used
 Data requirements are
reasonable
Weaknesses
 Relies on implicit assumptions –
may not be true
 Failure of implicit assumptions
may result in dramatically
incorrect results
 Too many parameters – fit data
well but result in large variance
in predictions
 No information available on
reliability of fit or error
distribution
 Haven’t really modeled the
underlying process
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