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Mathematics Seminar: "Chebyshev Bounds, Semidefinite Programming and European Call Option"
4:10pm; Neill 5W
Professor Hongbo Dong
Abstract: Semidefinite Programming (SDP) is a subfield of optimization where part of the decision variables involve (symmetric) positive semidefinite matrices. Polynomial-time (interior point) algorithms were found to solve SDPs to arbitrary precision. We will start with the basic formulations of SDP, its approximation of so-called Generalized Moment Problem. Then we describe two settings where SDP helps solve problems in other areas of mathematics: (1) computing the tightest bound for the probability inside of a quadratically constrained set; (2) pricing the so-called European Call Option; with the (only) assumption of moment information of random variables.