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Payandeh Najafabadi A, Sadri S. Approximating Bayes Estimator using Credibility Approach and Its Application to Determine the Irrigated Wheat’s Premium in Iran. QJIA 2015; 12 (43) :22-22
URL: http://journal.sbkiran.ir/article-1-25-en.html

In Actuarial science the usual credibility formula holds whenever, (i)
claim size distribution is a members of the exponential family of
distributions, (ii) prior distribution conjugates with claim size distribution,
and (iii) square error loss has been considered. As long as, one of these
conditions is violent, the usual credibility formula is no longer hold. This
article using the mean square error minimization technique develops a
simple and practical approach to the credibility theory. Namely, we
approximate the Bayes’ estimator with respect to a general loss function
and general prior distribution by a convex combination of the observation
mean and mean of prior, say, approximate credibility formula. Then this
article employs a well known and powerful maximum-entropy method
(MEM) for extending said results to a class of linear credibility, whenever
claim sizes have been distributed according to the logconcave
distributions. Namely, (i) it employs the maximum-entropy method to
approximate an appropriate Bayes’ estimator (with respect to either the
square-error or the Linex loss functions and general increasing and
bounded prior distribution) by a Linear combination of claim sizes; (ii) it
establishes that such an approximation coincides with the exact credibility
formula whenever the require conditions for the exact credibility are held.
Application to crop insurance has been given.