Credibility Theory

Buhlmann, Buhlmann-Straub, classical credibility, and empirical Bayes methods.

Key Concepts

• •Classical (limited fluctuation) credibility: full and partial credibility criteria
• •Buhlmann credibility: Z = n/(n + k) where k = expected value of process variance / variance of hypothetical means
• •Buhlmann-Straub model: extending Buhlmann to heterogeneous exposure volumes
• •Bayesian credibility: posterior distributions as exact credibility solutions
• •Conjugate prior families: Poisson-gamma, binomial-beta, normal-normal
• •Empirical Bayes: estimating structural parameters from the data
• •Credibility premium: Z * individual estimate + (1-Z) * group estimate
• •Nonparametric vs. semiparametric credibility methods
• •Applications in experience rating and premium adjustment
• •Connection between credibility and regression: random effects models

Study Tips

• 1.Understand the intuition behind the credibility formula before memorizing it.
• 2.Practice computing k (Buhlmann factor) from given process variance and hypothetical means.
• 3.Work through Buhlmann-Straub problems with different exposure volumes.
• 4.Connect credibility to Bayesian posterior means for a deeper understanding.
• 5.Practice both the formula and the concepts, as exams test both.

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