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 7 Ratemaking I
• September 15, 2009

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Agenda

• Ratemaking I
• Overall concept
• Two basic techniques
• Pure premium method
• Loss ratio method

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Ratemaking The Overall Concept
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Ratemaking Framework

• Ratemaking is an exercise in what-if
• What if an insurer wrote a book of policies
  similar to that which it wrote in the past?
• What if historical losses (or very similar ones)
  were to re-occur in the prospective policy
  period? How much would they cost the insurer?
• What if historical policies were re-written at
  current rates? What would be the premium?

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Ratemaking Framework (cont.)

• Is this what-if tenable?
• Must address inherent differences between
  anticipated future versus past
• Different types of policyholders / underwriting
• Different economic / financial environment
• Different judicial / legal atmosphere
• Different possible outcomes from stochastic
  processes
• Etc, etc.

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Ratemaking Framework (cont.)

• Premium
• Losses
• Expenses
• Load for Profit Contingencies

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Ratemaking Two Basic Techniques
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(1) Pure Premium Method

• Project future losses per unit of exposure
• This is the pure premium (PP)
• Calculate rate per unit of exposure
• Rate
• (PP FE) (1 VE Profit)
• FE fixed expenses () VE variable expenses()
• Profit profit and contingencies load ()

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(2) Loss Ratio Method

• Bring historical premiums to an on-level
  (current) basis
• Adjust historical losses for
• Loss development estimate what the insurer will
  ultimately pay out on losses from historical
  periods
• Loss trend adjust losses to reflect changes in
  claims costs over time
• Frequency (per unit of exposure) changes
• Severity (per loss) changes

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(2) Loss Ratio Method (cont.)

• Relate the trended and developed historical
  losses to the on-level premium
• Knowing expense and profit loads, this comparison
  will indicate whether or not, and to what degree,
  current rates need to be changed
• Adjust this indicated rate change, if necessary,
  for credibility considerations
• Take the above indicated overall rate change and
  spread it to multiple risk classifications and /
  or territories, if necessary

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Issues

• Data types and organization
• Losses paid, incurred,
• Premiums written vs earned, gross vs net
• AY vs PY vs CY
• Loss development
• Loss trend
• On-level premium
• Parallelogram method
• Classifications

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Next Time

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