Math 490 Casualty Actuarial Mathematics

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Math 490 Casualty Actuarial Mathematics

• Fall 2009
• University of Illinois at Urbana-Champaign
• Professor Rick Gorvett
• Session 9 Ratemaking III
• September 22, 2009

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Last Time

• Ratemaking II
• Trend vs development is there overlap?
• Basic vs total limits losses
• Parallelogram method

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Agenda

• Ratemaking III
• Putting it all together

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RecallRatemakingMethodologies
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Two Methods

• (1) Pure Premium Method
• Rate per unit of exposure
• (PP FE) (1 VE Profit)
• (2) Loss Ratio Method
• Actual (or experience) Loss Ratio ALR
• (trended developed losses) (on-level EP)
• Expected (or target) L/R ELR loss provision
  per 1 of rate (1-VE-Profit) (1G), where G
  ratio of non-premium-related expenses to losses
• Indicated rate change ALR ELR - 1

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Two Methods (cont.)

• (1) Pure Premium Method
• Based on exposures
• Produces rates directly
• No current / historical rates needed
• (2) Loss Ratio Method
• Based on premiums
• Produces an indicated rate change
• Needs current rates

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ExampleofRatemaking
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Data and Assumptions

• Use the Loss Ratio Method to determine the
  indicated rate change for policies to be sold
  from July 1, 2010, through June 30, 2011
• Use AY 2007 incurred loss data, evaluated as of
  December 31, 2009
• Annual policies
• VE 18, Profit 4, FE/PP 20

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Data and Assumptions (cont.)

• (All values in thousands)
• AY 2007 incurred loss _at_ 12/31/09 800
• 36-ult. LDF 1.250
• Loss trend 10 per year
• 2007 earned premium 1,600
• Rate changes since 1/1/06
• 12 on 10/1/07
• - 5 on 4/1/09

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Loss Ratio Method - Calculation

• (Note AY 2007 L/R
• Untrended and undeveloped 8001600 0.500
• Untrended (8001.250)1600 0.625)
• ELR (1-0.18-0.04) (10.20) 0.65
• ALR
• Numerator trended and developed losses
  8001.250(1.100)t
• What is t?

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L/R Method Calculation (cont.)

• ALR (cont.)
• Denominator is the 2007 EP, adjusted to an
  on-level basis
• I.e., what premium would be generated by writing
  the 2007 policies at 2010-11 rate levels?
• Parallelogram method
• Indicated rate change ALR ELR - 1