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Introduction to
Experience Rating
Mirage Re
Joy Takahashi - American Re Brokered Group
CAS Ratemaking Seminar
Session REI-47
March 12, 2001
Las Vegas, Nevada
1
Introduction to
Experience Rating
Mirage Re
Classical Burning Cost Method
 Frequency Based Method

2
Classical Burning Cost Method
Basic Steps
Mirage Re

Obtain large loss listing and calculate nominal
excess losses in layer (i.e. 100k xs 100k).

Apply trend factors; cap at policy limits.

Apply loss development factors.

Divide losses by adjusted subject premium to
derive an expected loss cost.
3
Classical Burning Cost
Step 1 - Collect data
Mirage Re
Log
1
5
6
14
19
38
Total
AY
96
96
96
97
98
00
Rptd Loss
255,692
75,324
130,235
1,152,028
175,274
360,044
Pol Limit
300,000
100,000
1,000,000
1,000,000
5,747,914
Loss in Layer
100,000
0
0
100,000
75,274
100,000
997,631
Note: Losses include ALAE. Not all losses are displayed.
4
Classical Burning Cost
Step 2 - Trend
Mirage Re
Log
1
AY
96
Trend
Factor
1.338
5
96
1.338
100,801
6
96
1.338
174,284
100,000
0
14
97
1.262
1,454,409
1,000,000
100,000
19
98
1.191
208,754
38
00
1.060
381,647
Total
Trended
Loss
342,174
6,907,025
Total w/ freq trend
Policy
Limit
300,000
Loss in
Layer
100,000
801
100,000
1,000,000
100,000
1,234,012
1,312,100
5
Classical Burning Cost
Step 3 - Loss Development
Mirage Re
AY
Trended
Loss in Layer
XS
LDF
Ultimate
Loss in Layer
96
251,500
1.238
311,300
97
300,100
1.485
445,600
98
212,200
2.302
488,500
99
442,700
4.604
2,038,100
00
105,500
41.432
4,370,300
Total
1,312,100
7,653,800
6
Classical Burning Cost
Step 4 - Divide by Subject Premium
Mirage Re
AY Adj SEP
Nominal
$
%
Trended
$
%
Tr & Dev
$
%
96
12,763
144.4 1.1%
251.5 2.0%
311.3
2.4%
97
18,233
215.5 1.2%
300.1 1.6%
445.6
2.4%
98
23,133
175.3 0.8%
212.2 0.9%
488.5
2.1%
99
26,460
362.5 1.4%
442.7 1.7% 2,038.1
7.7%
00
31,500
100.0 0.3%
105.5 0.3% 4,370.3 13.9%
Est ‘01 40,000
400.8 1.0%
533.6 1.3%
7
967.5
2.4%
Classical Burning Cost
Potential Problems
Mirage Re





Presence or absence of a few large claims drives the
indicated rates.
Order of application of development, trend and
capping makes a difference.
Trending individual claims past policy limits.
Impact of current policy limit profile vs. historicals.
History not reflective of current situation: reserving
practices, type of business, coverage, etc.
8
Frequency Based Method
Basic Steps






Mirage Re
Estimate # of claims above a data limit (e.g. 28
claims > $50,000).
Use size of loss curves to project # of claims above
the retention (e.g. 14.4 claims > $100,000 retention).
Distribute the projected counts by policy limit;
eliminate counts with policy limit below retention (e.g.
12.25 claims if 15% of exposure has $100,000 limits).
Use size of loss curves to project average severity of
claims in layer (e.g. $69,495 sev. in 100 x 100 layer).
Multiply frequency by severity to get total losses.
Divide by adjusted subject premium to get expected
loss cost.
9
Frequency Based
Step 1 - Project # of Claims Above Data Limit
Mirage Re
Detrended Actual
AYData Limit # > DDL
Freq
Trend
Clm Cnt
Dev Fctr
Projected
# > DL
96
37,363
6
1.104
1.050
6.96
97
39,605
8
1.082
1.155
10.00
98
41,981
5
1.061
1.559
8.27
99
44,500
13
1.040
2.339
31.63
00
47,170
5
1.020
5.847
29.82
Selected 50,000
28.00
10
Frequency Based
Step 1a - Selection Process
Mirage Re
Projected
AY # > DL
Adj SEP
Frequency
Projected
# @ 99 Levels
96
6.96
12,763
.545
21.8
97
10.00
18,233
.549
21.9
98
8.27
23,153
.357
14.3
99
31.63
26,460
1.196
47.8
00
29.82
31,500
.947
37.9
40,000
.700
28.00
Selected
11
Frequency Based
Step 2 - Project # of Claims Above Retention
Mirage Re
Limit
50,000
Projected
# > Ret.
28.00
Retention
xs
50,000
100,000
xs
100,000
14.41 *
300,000
xs
200,000
7.22 *
500,000
xs
500,000
2.84 *
* Note: these were derived from pareto size-of-loss curve
frequency formula: N X [(DL + B)/(R + B)] ^ Q
12
Frequency Based
Step 3 - Include Impact of Policy Limits
Mirage Re
Projected
Limit Retention # > Ret
50,000
# Clms by Pol Limit
100 300 500 1MM
New
# > Ret
50,000
28.00
4.20 5.60 7.00 11.20
28.00
100,000 100,000
14.41
2.16 2.88 3.60
5.76
12.25
300,000 200,000
7.22
1.08 1.44 1.81
2.89
6.14
500,000 500,000
2.84
1.14
1.14
.43
.57
.71
‘01 Policy Limit Distribution: 15% 20% 25% 40%
Note: Claims below line are eliminated from the layer due to policy limits.
13
Frequency Based
Step 4 - Estimate Loss $ in Layer
Mirage Re
Limit
Retention
Projected
# > Ret.
Avg Sev.
in Layer
Loss Cost
in Layer
100,000 100,000
14.41
69,495
1,001,423
100,000 100,000
12.25
69,495
851,210
Note: Average severities are from pareto size-of-loss curve
severity formula: [(R+B)/(Q-1)] X {1 - [(R+B)/(R+L+B)]^(Q-1)}
14
Frequency Based Method
Step 5 - Divide by Subject Premium
Mirage Re
Subject
Earned Prem.
40,000,000
Selected Loss Cost
$
%
851,210
15
2.1%
Frequency Based Method
Potential Problems
Mirage Re




Credibility of claim count development factors
Adjustment of development factors by data
limit
Picking an appropriate data limit
Testing of size-of-loss assumptions
16
Frequency Based Method
Advanced Techniques
Mirage Re
Goal: Fitting individual claim data to size-of-loss curve.
» Trend individual claims to common accident date.
» Develop trended individual claims to ultimate, using
report year development factors if available.
» Fit developed and trended claims to size-of-loss curve.
» Test curve with actual data and industry curves.
» Use new fitted curve in frequency based method to
derive new loss cost.
17
Frequency Based Method
Advanced Techniques
Mirage Re
Comparison of Actual and Fitted Average Severities (in 000’s)
140
Average Severity
120
100
80
60
40
20
0
200
400
600
800
1000
Actual
1200
1400
Pareto
18
1600
1800
2000
2200
Experience Rating
Comparison of Methods
Mirage Re
Classical Burning Cost
Est. Losses $
Est. Loss Cost %
Original
1,089,100
2.7%
Alternative
967,500
2.4%
Original
851,210
2.1%
Co. Fitted
955,118
2.4%
1,000,000
2.5%
Frequency Based Mtd
Est. Losses $
Est. Loss Cost %
Selected
19