October 2014
Intermediate to advanced
584 pages
22h 2m
English
Content preview from Pricing in General Insurance
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447Credibility Theory
25.6 Questions
1. Using the Bayesian approach to credibility, prove that the posterior distribution of
Θ given
s
(see Section 25.4.2 for the meaning of these parameters) is itself a normal
distribution with these parameters:
Θ
Θ
|~ ,sN
ns
nn
σσ
σσ
σσ
σσ
cm
cm
cm
cm
22
22
22
22
+
++
2. Prove that Bayesian credibility estimate – when the number of claims of a client
follows a Poisson distribution and the prior distribution for the Poisson rate fol-
lows a gamma distribution – can be expressed in the standard format of Equation
25.17.
3. State the formula for the credibility value Z used in the uncertainty-based cred-
ibility model ...
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