A.3. Bailey & Simon - PPV Credibility

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  1. Merit rating
    • # full years since most recent accident / licensed date
    • A, X, Y, B = 3+, 2, 1, 0 years
    • A+X = experience for 2+ accident-free years
    • Premium = Base x Merit Factor x Other Rating Variables
  2. Experience rating formula
    • credibility weighted LR = Z x actual LR + (1 - Z) x expected LR
    • Experience Mod = R + (1 - Z), Z = credibility, R = ratio of actual to expected losses
    • Z depends not only on the volume of data but also on amount of variation within the class
  3. B&S Method to Calculate Mod
    • use frequency to premium instead of LR = same as assuming constant severity
    • (# claims with rating) / (on-level EP for rating at present “B” rates) divided by
    • (# claims in total for class) / (class total on-level EP at present “B” rates)
  4. Bailey & Simon methodology to calculate R
    • infer or estimate what R would’ve been for the prior term (1 year)
    • either risk is A, X, Y so had no claim therefore R = 0, Mod = 1 - Z
    • or risk is B and we approximate R as 1 / (1 - e) using car years instead of premium, with λ = # claims / earned car years
    • plug Mod and R in the formula to solve for Z
  5. Credibility vs number of years claims free
    • if an individual insured's chance for an accident remained constant year to year and
    • if there were no risks leaving or entering the class then
    • credibility for experience would vary in proportion of the amount of years
  6. Maldistribution (exposure correlation)
    • B&S are specifically concerned with correlation between territory variable and merit rating variable, i.e. high frequency territories producing more X, Y, B and higher premium
    • Once we correct for it by using premium as a base for frequency instead of exposure:
    •    high frequency territories are also high rate territories 
    •    territorial differential are proper (e.g. same loss ratio across all territories)
  7. Paper conclusions
    • experience for one car for one year has significant and measurable credibility
    • in a highly refined PPV rating classification, credibility would be low
    • the credibility for varying years of experience should increase in proportion to the # years of experience
  8. Bühlmann credibility
    • suppose X is a random variable with distribution parameter Θ
    • Θ itself is a random variable with some distribution
    • credibility of sample of n is Z = n / (n + k)
    • k = E[Var(X|Θ)] / Var[E(X|Θ)] = exp value of process var / var of hypothetical means
    • if X ~ Poisson(λ) and λ ~ Normal(μ,σ2) then k = E[λ] / Var[λ] = μ / σ2
  9. Poisson Formula
    Pr(X = k) = λke-k / k!

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A.3. Bailey & Simon - PPV Credibility
2015-09-04 12:06:36
PPV Credibility Bailey Simon

Bailey & Simon PPV Credibility
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