Introduction to Reinsurance Exposure Rating

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Introduction to Reinsurance Exposure Rating
CAS Ratemaking SeminarSession REI-47March 12,
2001 - Las Vegas
Ira Kaplan ikaplan_at_gcr.com
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Exposure Rating ObjectivesEstimate Expected
Excess Losses

• Analyze the premium profile
• Estimate the expected loss ratio
• Estimate the layering of the expected losses

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Treaty SubmissionInformation Needed

• Premiums by policy limits
• What business exposes the layer to loss?
• Premiums by G.L. class code
• How does the business expose the layer to loss?
• Historic loss ratios
• This takes us from premiums to losses

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Exposure Rating AssumptionsPolicy Limits
Profiles

• Premium Distribution by Policy Limit
• Limit Est. 01 Premium of Total
• 100/100 7,000,000 17.5
• 300/300 8,520,000 21.3
• 500/500 10,000,000 25.0
• 1000/1000 14,480,000 36.2
• 40,000,000

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Exposure Rating AssumptionsGL class profiles

• 100 Premises/Operations
• 100 Table 2

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Distribution of Premium to Layer

• Premium Distribution by Policy Limit
• Limit Premium Retention 100 Xs100 Xs 200
• 100/100 7,000 7,000 0 0
• 300/300 8,520 6,842 1,066 612
• 500/500 10,000 7,379 1,150 1,471
• 1000/1000 14,480 9,641 1,502 3,336
• 40,000 30,862 3,717 5,420
• NOTE All values in thousands

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The distribution of losses to layer is not the
same as the distribution of premiums to layer

• - alae
• - risk load

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Distribution of Premium and Expected Loss to
Layer Policy Limit 500/500

• Premium Loss
• Layer Distribution Distribution
• 0-100 73.8 67.8
• 100-200 11.5 14.7
• Above 200 14.7 17.5

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Selection of Direct ELR

• Review historic experience
• Test reserve adequacy
• Understand business plan changes
• Review rate level changes
• Selection 40 (excl. alae)

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Allocation of Premium Loss to Layer

• Limit Retention 100 Xs100 Xs200 Total
• 100/100 Premium 7,000 0 0 7,000
• Loss 2,800 0 0 2,800
• 300/300 Premium 6,842 1,065 612 8,520
• Loss 2,551 552 304 3,408
• 500/500 Premium 7,379 1,150 1,472 10,000
• Loss 2,714 588 698 4,000
• 1000/1000 Premium 9,641 1,502 3,336 14,480
• Loss 3,537 766 1,485 5,792
• Total Premium 30,862 3,717 5,421 40,000
• Loss 11,602 1,907 2,490 16,000

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ALAE and combination losses need to be included
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ALAE by Layer

• Retention 100 Xs100 Xs200 Total
• Premium 30,862 3,717 5,421 40,000
• ExpLoss 11,603 1,907 2,490 16,000
• ALAE 42.9 20.9 18.6 36.6
• ALAE 4,988 398 465 5,851
• LossALAE 16,591 2,304 2,956 21,851
• LLAE Ratio 53.8 62.0 54.5 54.6

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Loss Ratios by Layer
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Expected Frequency Severity for 100,000 Layer

• Expected Loss 1,906,650
• Expected Avg Severity 68,207
• Expected of Claims 27.95

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How to Test the Exposure Rating Indications

• Review the premium profile selections
• Review the selected ELR
• Consider the appropriateness of the ISO loss
  curves
• Look at actual loss information
• Experience Rating

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Pro Rata ALAE

• Loss ALAE L ALAE
• Total 640 320 960
• 600 x 400 240 120 360
• Ceded Loss x Direct Expenses Ceded Loss
• Direct Loss
• Ceded Loss x (Direct Expense Direct Loss)
• Direct Loss
• Ceded Loss x ( 1 Direct Expense )
• Direct
  Loss

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ALAE Treatment - case 1
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ALAE Treatment - case 2
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ALAE Load Can Vary

• By layer - as seen earlier
• Model with two way variability
• Load decreases by limit
• ALAE is then allocated to layers
• One allocation formula for Pro Rata
• A more complicated one for Added To

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Introduction to Reinsurance Exposure Rating?
NOT!

• Intro to Excess of Loss Reinsurance Exposure
  Rating approach to estimating LossALAE for GL
• Basics of Reinsurance Pricing by David R.
  Clark, Exam 6 Study Note

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Basics of Reinsurance Pricing

• Proportional Treaties
• Property Per Risk XS
• Casualty Per Occurrence XS
• WC, Umbrella, AADs
• Aggregate Distributions
• Property Cat
• Final Price -
• risk loads, expenses, etc.