Consider the problem of finding optimal bounds on the expected value of piece-wise polynomials over all measures with a given set of moments. We show that this problem can be studied within the framework of conic programming. Relying on a key approximation result for conic programming, we show that these bounds can be numerically computed or approximated via semidefinite programming. Also, we illustrate how our approach can be applied to problems in probability, finance and inventory theory.
Mathematics of Operations Research 30 (2005) pp. 369--388.