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Optimal moment bounds for special classes of continuous distributions via semidefinite programming

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The author provides an optimization framework for computing optimal upper and lower bounds on functional expectations of distributions with special convex cone properties, given moment constraints. Bertsimas and Popescu (4, 5) have already shown how to obtain optimal moment inequalities for arbitrary distributions via semidefinite programming. These bounds are not sharp if the underlying distributions process additional structural properties, such as symmetry, unimodality, convexity, smoothness. The author uses conic duality to show how optimal moment bounds for such convex classes of distributions can be efficiently computed as semidefinite programs. She also characterizes the corresponding sets extremal distributions that achieve these bounds. In particular, she obtains closed from generalizations of Chebyshev's inequality for symmetric and unimodal distributions.

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en

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application/pdf

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http://flora.insead.edu/fichiersti_wp/inseadwp2001/2001-64.pdf

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Copyright INSEAD. All rights reserved