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A Semidefinite Programming Approach to Moment Problems

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Abstract:
We present an optimization framework for obtaining optimal upper and lower bounds on functional expectations of a random variable given moment constraints. We prove that a very general class of such moment problems can be efficiently solved, or approximated, by semidefinite programs (SDP). Our results rely on recently established connections between the theory of positive polynomials and semidefinite programming. Using conic duality, we incorporate structural distributional properties, such as symmetry and unimodality into the SDP formulation of the moment problem. In particular, we obtain several closed form extensions of Chebyshev's inequality. We discuss applications in finance, statistical estimation, inventory control.

Type of Seminar:
Public Seminar
Speaker:
Dr. Ioana Popescu
INSEAD
Date/Time:
Nov 26, 2001   17:15
Location:

ETH Zentrum, Gloriastrasse 358006 Zurich, ETZ E6
Contact Person:

Prof. P. Parrilo
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Biographical Sketch:
Ioana Popescu joined the Decision Sciences group at INSEAD in 1999, after graduating from MIT with a PhD in Applied Mathematics and Operations Research. Her research interests include moment problems, convex and robust optimization, target-based risk analysis and revenue management.