A conic programming approach to generalized Tchebycheff inequalities

A conic programming approach to generalized Tchebycheff inequalities

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Article ID: iaor20061413
Country: United States
Volume: 30
Issue: 2
Start Page Number: 369
End Page Number: 388
Publication Date: May 2005
Journal: Mathematics of Operations Research
Authors: ,
Keywords: Programming (cone), programming (semidefinite)
Abstract:

Consider the problem of finding optimal bounds on the expected value of piecewise polynomials over all measures with a given set of moments. This is a special class of generalized Tchebycheff inequalities in probability theory. We study this problem within the framework of conic programming. Relying on a general approximation scheme for conic programming, we show that these bounds can be numerically computed or approximated via semidefinite programming. We also describe some applications of this class of generalized Tchebycheff inequalities in probability, finance, and inventory theory.

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