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Moment problems via semidefinite programming: applications in probability and finance

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The goal of this paper is twofold: first, to present the beautiful interplay of optimization and moment inequalities, from a modern perspective, motivated by problems in probability and finance. second, to characterize the complexity of deriving tight moment inequalities, search for efficient algorithms in a general framework, and, when possible, derive simple closed-form bounds. The authors use semidefinite and convex optimization methods to derive optimal bounds on the probability that a multivariate random variable belongs in a given set, when some of the moments of the random variable are known. In the finance context, they use the same approach to find optimal bounds for option prices with general payoff given only moments of underlying asset prices, and without assuming any model for the underlying price dynamics.

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en

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application/pdf

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http://flora.insead.edu/fichiersti_wp/inseadwp2000/2000-27.pdf

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Copyright INSEAD. All rights reserved