Credibility Theory

Credibility theory answers the central reinsurance-pricing question: how much to trust the cedant's own experience. The credibility premium blends the observed mean \$\bar X\$ with the collective (market) mean \$\mu\$:

Credibility premium

$$P=Z\,\bar X+(1-Z)\,\mu$$

In Bühlmann's model, the credibility factor \$Z\$ depends on the number of observations \$n\$, the expected process variance \$v=E[\operatorname{Var}(X\mid\Theta)]\$ and the variance of hypothetical means \$a=\operatorname{Var}(E[X\mid\Theta])\$:

Bühlmann credibility factor

$$Z=\frac{n}{n+k},\qquad k=\frac{v}{a}$$

More data (n up) or more heterogeneity between risks (a up) increases the weight on own experience.

The Bühlmann-Straub extension allows different exposure volumes \$m_i\$ per period, the natural setting for reinsurance, where years differ in size:

Bühlmann-Straub

$$Z=\frac{m}{m+k},\qquad m=\sum_i m_i$$

Credibility grows with total exposure volume, weighting each period by its size.

Why it matters

Credibility is exactly how Power Re blends experience and exposure rating, disciplined, defensible and rating-agency friendly.

Credibility Theory

Why it matters

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