# 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!

### Card Set Information

 Author: EExam8 ID: 304933 Filename: A.3. Bailey & Simon - PPV Credibility Updated: 2015-09-04 12:06:36 Tags: PPV Credibility Bailey Simon Folders: Description: Bailey & Simon PPV Credibility Show Answers:

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