Abstract
Abstract In this paper we show how to obtain tight upper and lower bounds on E[h(X)] for a given function h, and a bounded random variable X with three known integral moment constraints. The improvement possible when we have the additional knowledge that X is unimodal is also discussed. We show how these bounds can be used in calculating the probability of ruin, and setting initial reserve levels when we have only incomplete information concerning the statistical distribution of the loss variable, in developing envelope estimates for the class of commonly used utility functions using only the values assessed at finitely many points, and other applications.
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