Intro to Credibility

Section 1 of Exam MAS-II

Collective Risk Model: Aggregate Premium Equation

Aggregate premium mean and variance

Full Classic (Limited Fluctuation) Credibility Condition

S bar = Sample mean

Miu_S = Expected mean

k = accuracy parameter

1 - alpha = Coverage Probability

Convert between full credibility standard for n_e and n_c

Full credibility formula table for PP, Freq, and Sev with n_c and n_e

Updated prediction of loss for partial credibility

D = Observed

M = Manual Rate

Z = Credibility Factor

Square root rule for calculating Z

n = actual exposures

n * miu_N = avg claims for n exposures (use actual number of claims for sev or if miu_N is unknown)

Model Distribution: Discrete vs Continuous

Posterior Distribution: Discrete vs Continuous

Remember to check if a common distribution can be recognized from f(data | theta) * pi(theta) and the domain. Recognizing a distribution allows us to avoid integration and save time.

Predictive Distribution: Discrete vs Continuous

Loss Functions: 3 Types with 3 Bayesian Estimates

Loss Function Formulas

Conjugate Prior Types

Plus Uniform (0, theta) - SP-Pareto

Conjugate Prior: Poisson-Gamma

Conjugate Prior: Poisson-Gamma (1/theta)

Conjugate Prior: Exponential-Gamma

Conjugate Prior: Exponential-Inverse Gamma

Conjugate Prior: Binomial-Beta

Conjugate Prior: Geometric-Beta

Convert Geometric from mean-based (B) to probability-based (q)

Steps to solving a Buhlmann credibility problem

Uniform Exposures: Hypothetical mean, Process Variance mean, and Variance of Hypothetical Mean Equations

Miu_x is x bar

Non-Uniform Exposures: Hypothetical mean, Process Variance mean, and Variance of Hypothetical Mean Equations

Credibility-Weighted Mean (EHM)

Also called method to “preserve total losses/claim count”

Best way to identify the number of exposures (n) for the Z equation

Think “what is the denominator for x bar” for whatever the question is asking about (could be a single policyholder)