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 10 Risk Classification
• September 24, 2009

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Agenda

• Ratemaking relativities
• Risk classification

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Ratemaking Relativities

• Three kinds of relativities
• Classification
• Territorial
• Increased limits
• Classification ratemaking
• One class serves as the base class (relativity
  1.00)
• Rates for other classes are keyed off of the base
  class rate
• Class rate base rate class relativity factor

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Ratemaking Relativities (cont.)

• Classification ratemaking (cont.)
• Ratemaking process
• Determine indicated overall rate change
• Determine on-level premium for each class
• Convert on-level EP by class to a
  base-class-equivalent by dividing by the existing
  class relativities
• Determine loss ratio for each class, using
  base-class-equivalent on-level EP
• Determine indicated class relativities by
  dividing each classs loss ratio by the base
  class loss ratio
• Use an off-balance factor to determine the base
  rate necessary to achieve the overall indicated
  rate change
• If necessary, limit rate changes by class to any
  existing regulatory restrictions, and adjust to
  yield the overall indicated rate change

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Ratemaking Relativities (cont.)

• Territorial ratemaking
• Very similar to classification ratemaking,
  conceptually and procedurally
• Increased limits factors
• Basic limits premium or loss cost
• E.g., 100,000 per occurrence limit
• Calculate premiums or loss costs for higher
  policy limits by multiplying the basic limits
  value by the appropriate increased limits factor
  (ILF)

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Risk Classification

• Differential premiums
• Group characteristics determine the class
• Different characteristics imply different
  underlying loss propensities, and thus different
  indicated / required premiums
• Costs that may vary by group
• Losses
• Risk variation from expected values e.g.,
  more heterogeneity within a group implies more
  potential adverse selection
• Expenses
• Investment income e.g., long- versus
  short-tailed LoBs

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Risk Classification Rating Variables

• Criteria for selecting rating variables
• Statistical or actuarial
• Accuracy and fairness
• Homogeneity
• Credibility
• Reliability or predictive stability
• Operational or practical
• Objectively defined
• Administrative expense
• Verifiability

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Rating Variables (cont.)

• Criteria for selecting rating variables (cont.)
• Social
• Socially acceptable
• Privacy issues
• Causality intuitively understandable underlying
  economic or risk management link of rating
  variable to insurance cost
• Controllability
• Affordability
• Legal
• State regulations
• Federal equal protection clause

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2006 CAS Exam 5, 39
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2004 CAS Exam 5, 36