1

Mirage Re

Introduction to Experience Rating

Joy Takahashi - American Re Brokered Group

CAS Ratemaking SeminarSession REI-47 March 12, 2001

Las Vegas, Nevada

2

Mirage Re

Introduction to Experience Rating

Classical Burning Cost Method Frequency Based Method

3

Mirage Re

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.

4

Mirage Re

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.

5

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

6

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

7

Mirage Re

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%

8

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.

9

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.

10

Mirage Re

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

11

Mirage Re

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

12

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

13

Mirage Re

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.

14

Mirage Re

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)}

15

Mirage Re

Frequency Based MethodStep 5 - Divide by Subject Premium

Subject Selected Loss Cost Earned Prem. $ %

40,000,000 851,210 2.1%

16

Mirage Re

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

17

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.

18

Mirage Re

Frequency Based MethodAdvanced Techniques

20

40

60

80

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)

19

Mirage Re

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%