1 Mirage Re Introduction to Experience Rating Joy Takahashi - American Re Brokered Group CAS...
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1
Mirage Re
Introduction to Experience Rating
Joy Takahashi - American Re Brokered Group
CAS Ratemaking SeminarSession REI-47 March 12, 2001
Las Vegas, Nevada
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Mirage Re
Introduction to Experience Rating
Classical Burning Cost Method Frequency Based Method
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Classical Burning Cost MethodBasic Steps
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.
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Classical Burning CostStep 1 - Collect data
1 96 255,692 300,000 100,000 5 96 75,324 0 6 96 130,235 100,000 014 97 1,152,028 1,000,000 100,00019 98 175,274 75,27438 00 360,044 1,000,000 100,000
Total 5,747,914 997,631
Log AY Rptd Loss Pol Limit Loss in Layer
Note: Losses include ALAE. Not all losses are displayed.
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Mirage Re
Classical Burning CostStep 2 - Trend
Trend Trended PolicyLoss inLog AY Factor Loss Limit Layer 1 96 1.338 342,174 300,000 100,000
5 96 1.338 100,801 801
6 96 1.338 174,284 100,000 0
14 97 1.262 1,454,409 1,000,000 100,000
19 98 1.191 208,754 100,000
38 00 1.060 381,647 1,000,000 100,000
Total 6,907,025 1,234,012
Total w/ freq trend 1,312,100
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Mirage Re
Classical Burning CostStep 3 - Loss Development
Trended XS UltimateAY Loss in Layer LDF Loss in Layer96 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
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Classical Burning CostStep 4 - Divide by Subject Premium
Nominal Trended Tr & DevAY Adj SEP $ % $ % $ %
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% 967.5 2.4%
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Mirage Re
Classical Burning CostPotential Problems
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.
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Mirage Re
Frequency Based MethodBasic Steps
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.
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Frequency BasedStep 1 - Project # of Claims Above Data
Limit
Detrended Actual Freq Clm Cnt ProjectedAY Data Limit # > DDL Trend Dev Fctr # > 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
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Frequency BasedStep 1a - Selection Process
Projected ProjectedAY # > DL Adj SEP Frequency # @ 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
Selected 40,000 .700 28.00
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Mirage Re
Frequency BasedStep 2 - Project # of Claims Above
Retention
Projected Limit Retention # > Ret. 50,000 xs 50,000 28.00
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
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Frequency BasedStep 3 - Include Impact of Policy Limits
Projected # Clms by Pol Limit New Limit Retention # > Ret 100 300 500 1MM # > Ret
50,000 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 .43 .57 .71 1.14 1.14
‘01 Policy Limit Distribution: 15% 20% 25% 40%
Note: Claims below line are eliminated from the layer due to policy limits.
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Frequency BasedStep 4 - Estimate Loss $ in Layer
Projected Avg Sev. Loss CostLimit Retention # > Ret. in Layer 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)}
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Frequency Based MethodStep 5 - Divide by Subject Premium
Subject Selected Loss Cost Earned Prem. $ %
40,000,000 851,210 2.1%
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Frequency Based MethodPotential Problems
Credibility of claim count development factors Adjustment of development factors by data
limit Picking an appropriate data limit Testing of size-of-loss assumptions
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Mirage Re
Frequency Based MethodAdvanced Techniques
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.
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Mirage Re
Frequency Based MethodAdvanced Techniques
20
40
60
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100
120
140
0 200 400 600 800 1000 1200 1400 1600 1800 2000 2200
Aver
age
Seve
rity
Actual Pareto
Comparison of Actual and Fitted Average Severities (in 000’s)
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Experience RatingComparison of Methods
Classical Burning Cost Original AlternativeEst. Losses $ 1,089,100 967,500Est. Loss Cost % 2.7% 2.4%
Frequency Based Mtd Original Co. FittedEst. Losses $ 851,210 955,118Est. Loss Cost % 2.1% 2.4%
Selected 1,000,000 2.5%