Sn 207-00 An Examination Of Bayesian Credibility Topics

Front 1

Properties of a System That Affect Bayesian Credibility

Back 1

(1) The greater the number of observations, the higher the credibility of the observations.
(2) The smaller the process variances, the higher the credibility of the observations.
(3) The greater the variance of the distribution of hypothetical means, the higher the credibility of the observations.

Front 2

DEFINITION AND FORMULA FOR BAYESIAN CREDIBILITY

Back 2

 Given n observations (n exposure units) and some underlying processes,

________n_____________________________
Credibility Z = [expected value of] process variance
n + variance of hypothetical means

Then:

 Weight the observations vs. the prior assumptions by Z and 1 – Z, respectively.

C = Z*R + (1-Z)*H

Compromise = Z * Real observations + (1-Z) * Prior Hypothesis.

 Apply judgment and practical considerations, too.

Front 3

Classical (traditional) vs. Bayesian Credibility
Classical:

Back 3

 use confidence intervals
 determine # observations needed for 100% credibility
 assign the complement to prior knowledge

Front 4

Bayesian:

Back 4

 formulas as above.
 preferable
 but difficult to understand & apply

Front 5

APPLICATIONS OF CREDIBILITY THEORY TO INSURANCE COMPANY OPERATIONS

Application of Credibility to Experience Rating
(see GI 33 for an introduction to experience rating)

Back 5

 Universe is all possible insurable risks (policyholders)
 Assume the risks belong to distinct classes.
 select a risk at random and classify (underwrite) it.

 “Manual Rate” = average for its class
 Next year’s rate = credibility-weighted average of observed experience vs. manual rate
 The lower the credibility, the better the risk classification system (meaning the classes are homogeneous)

Moral: High credibility isn’t necessarily “good”.

Front 6

Application of Credibility to Ratemaking

Back 6

 Insurer wants to set new premium rates for each class.
 The overall increase must be allocated among the classes.
 The higher each class’s credibility, the better the underlying rate classification system is.


Done.