INTRODUCTION TO REINSURANCE
EXPERIENCE AND EXPOSURE RATING
SUMMARY AND RECONCILIATION OF ESTIMATES
MICHAEL E. ANGELINA - TOWERS PERRIN
CAS RATEMAKING SEMINAR
MARCH 11, 2004
PHILADELPHIA, PA
KEY ASSUMPTIONS
You are the underwriter/actuary of the assumed
reinsurance division, what should you be thinking
about:
 Hazard group selection
 Loss ratios
 Expense loadings
 Claim frequencies
 Tail factors
 Layer severities
 Credibility of experience
 Results of u/w audit
2
Reconciliation of Estimates
Goal - determination of a final estimate
Recap of results




Exposure Estimate
Classical Burning Cost
Freq/Severity-Industry
Experience Estimate
Expected
Counts
2.3
1.09
0.85
0.96
Ultimate
Loss & ALAE
82.1
68.4
69.5
67.7
Excess
Severity
28.0
15.9
12.3
14.2
Wide range of results between experience and exposure
 Severity relatively flat
 Variation in expected counts/losses
3
Experience Rating - Frequency Based Method
Projected # of Claims for Rating Year
(1)
(2)
Accident
Year
Detrended
Data
Limit
6.0%
1999
2000
2001
2002
2003
74,726
79,209
83,962
89,000
94,340
Total All yrs
Total 99-02
Rate Year 2004
(3)
Actual #>
Detrended
Data
Limit
Frequency
Trend
@ 2%
(5)
Claim
Count
Dev't
Factors
4.0
7.0
2.0
9.0
2.0
1.104
1.082
1.061
1.040
1.020
1.125
1.238
1.671
2.506
6.265
24.0
22.0
100,000
(4)
(6)
(7)
Adjustment
for Growth
in Premium
Projected
# of Claims
>Data Limit
[3x4x5x6]
2.960
2.162
1.684
1.509
1.270
14.7
20.3
6.0
35.4
16.2
92.6
76.3
20.00
4
RECAP OF ESTIMATES
Ultimate Losses
4,000
Dollars (000s)
3,000
2,000
1,000
0
1999
Reported
2000
2001
Indicated Ultimate Losses
2002
Exposure
2003
Burning
Cost
Experience
5
RECAP OF ESTIMATES
Expected Counts > $100k
40
35
Dollars (000s)
30
25
20
15
10
5
0
1999
Reported
2000
2001
Indicated Ultimate Losses
2002
Exposure
2003
Burning
Cost
Experience
6
Reconciliation of Estimates
 Which method yields best estimate?
 Experience estimates
 Test at lower layers
 Results for frequency/severity and burning cost should be consistent
 Considerations
 credibility of data - 40 XS claims?
 loss development factors - reflecting claim audit?
 load for ALAE (explicit/implicit?)
 adjust for claim impact of premium growth - deterioration in U/W?
 account for change in policy limits?
7
Reconciliation of Estimates
 Which method yields best estimate (con’t)
 Exposure estimates
 Allocation of premium consistent with company’s
 Historical comparison of XS premium to losses
 suggest different loss ratio for layer?
 Considerations
 appropriateness of size of loss curve
 test with claim emergence at different attachment points
 calculate implied claim counts to company experience
 compare industry curve to company fitted curve
 fitting curve is not trivial (development on individual claims)
 adequacy of loss ratio
 reflect claim audit findings
 adjust for implication on growing business
 account for differences in excess layer vs. primary layer
8
1.3
1.2
1.1
1.0
0.9
0
2,
00
0
1,
50
0
1,
00
75
0
50
0
45
0
40
0
35
0
30
0
25
0
20
0
15
0
0.8
10
0
Limited Average Severity
Reconciliation of Estimates
Policy Limit
Ind-M L
Ind-M
Act
9
Reconciliation of Estimates
Expected Claim Counts
60
50
40
30
20
10
0
50
75
100
150
200
> 250
Attachment Point
Exposure
F/ S - Industry
F/ S - Company
Actual
10
Audience Underwriting
Recap of Results
Ultimate
Exp Counts
ALAE
Implied
Loss & ALAE
>100k
Load
XS L/R
Exposure
2.30
28.0
21%
62.1%
Burning Cost
1.09
15.9
8.5%
31.8%
Frequency/Severity
0.85
12.3
7.5%
24.6%
1.00
14.0
8.0%
29.1%
(Industry)
Experience
* assumes premium allocated to layer is 3,717 (from exposure method)
11
Reconciliation of Estimates
 Goal - Sensitivity test indications
 Experience Indications (burning cost)
 Selected
1,000
 Alter Selection
1,200
 ALAE Differences
111
 Revised Selection
1,311
2.5%
BF: 2 recent yrs
18% vs 8%
3.3%
 Experience Indications (frequency / severity)
 Selected
851
2.4%
 Alter Selection
1,080
Different weights
 ALAE Differences
105
18% vs 7.5%
 Revised Selection
1,185
3.0%
 Final Selection
1,250
3.1%
12
Reconciliation of Estimates
 Goal - Move expected ultimates to similar base
 Exposure Indications
 Selected
2,304
 Alter Selection
1,593
 ALAE Differences
(40)
 Revised Selection
1,553
5.8%
higher % Table 1
18% vs 21%
3.9%
 Experience Indications (Selected)
 Revised Selection
1,250
3.1%
 implied loss ratio for layer
 Final Selection
1,450
 implied loss ratio for layer
34.4%
3.625%
39%
13
Reconciliation of Estimates Scenario Testing
 Move away from point estimate of methods and look at a range of
possible outcomes
 Exposure
 size of loss table/loss ratio
 what assumptions would get result to experience rate
 20% loss ratio, lower hazard curve, less ALAE loading, combination
of all three
 Experience
 LDF’s, claim counts, size of loss curve (industry or company)
 what assumptions get result to exposure rate
 54 claims above 50k, heavier tail factor (1.238 @ 60 months to 2.2)
 Assign weights to various outcomes and determine a new
expected loss estimate
 Credibility
14
Reconciliation of Estimates
 Leads to stochastic applications
 Need to assign probabilities to various assumptions/scenarios
 Think about independence of variable
 Address parameter/process risk
 Results in better pricing for AAD considerations, swing plans, stop
loss treaties, etc.
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