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The maximum entropy principle is a powerful tool for solving underdeterminedinverse problems. This paper considers the problem of discretizing a continuousdistribution, which arises in various applied fields. We obtain theapproximating distribution by minimizing the Kullback-Leibler information(relative entropy) of the unknown discrete distribution relative to an initialdiscretization based on a quadrature formula subject to some momentconstraints. We study the theoretical error bound and the convergence of thisapproximation method as the number of discrete points increases. We prove that(i) the theoretical error bound of the approximate expectation of any boundedcontinuous function has at most the same order as the quadrature formula westart with, and (ii) the approximate discrete distribution weakly converges tothe given continuous distribution. Moreover, we present some numerical examplesthat show the advantage of the method and apply to numerically solving anoptimal portfolio problem.Comment: 20 pages, 14 figure

Error estimate and convergence analysis of moment-preserving discrete approximations of continuous distributions