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Credibility

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    • Use CSLC to lookup the credibility, MSL and EER from the ISO tables
      • Looking up the tables is not part of Exam 5. But we may be asked to calculate the credibility or calculate the EER given the numerator and denominator.

    • 3 necessary criteria

    • 0≤Z≤1

    • Z should increase as n increases (dZ/dn≥0).
    • Z should increase as n increases at a decreasing rate (d/dn(Z/n)<0).

    • Methods

    • Classical

      • Z×Observed+(1−Z)×Related Experience
      • Partial
        • Claim counts (n): Z=min(n/N0​​,1)
        • Exposures: Z=min(e/(N0​/F)​,1)
          • Exposures for full credibility = N0​/expected frequency(F).
    • Buhlmann
      • Least Squares Credibility.
      • Estimate = Z×(Observed Experience)+(1−Z)×Prior Mean
      • And Z=N/(N+K)
        • K=EVPV / VHM
          • Expected Value of Process Variance, EVPV = E[Var(X)].
          • Variance of Hypothetical Means, VHM = Var(E[X]).
    • Bayesian Analysis

Complement of Credibility

Properties

  • Accurate (close to target).
  • Unbiased (on target on average).
  • Statistically independent from base statistic.
  • Available (else not practical).
  • Easy to compute (else difficult to justify).
  • Logical relationship to base statistic (" " " justify).

Complements in First Dollar Ratemaking

Ground up losses (or small deductibles): Loss Cost (LC).

  • LC of a Larger group including subject group
    • Regional or Countrywide for state data.
    • May be biased.
      • There is a reason why the subject group has been separated from the larger group.
  • LC of a larger related group
    • Usually biased.
    • Logical relationship if chosen reasonably.
  • Rate change from large group applied to present rates
    • Adjusted version of prior complement to reduce bias.
    • Complement = Current LC (Subject) * (Large group Ind LC / Large group Current Avg LC).
  • Harwayne's method
    • We are trying to find the complement of credibility for LC (Pure premium) of class A.
    • Calculate A's, B's, C's average pure premium by using Class A's exposures as the weight.
    • Calculate adjustment factor (Class B / Class A avg premium).
    • Multiply PP for each class by adjustment factor.
    • Exposure weight the PP of the other classes to get the complement.
  • Trended Present rates #todo
  • Competitor's rates
    • Biased, inaccurate, and difficult to obtain.

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