MIT Department of Electrical Engineering & Computer Science

"Moment Problems and their applications in Probability Theory, Finance, Stochastic Networks and Partial Differential Equations"

Prof. Dmitris Bertsimas
MIT Sloan, OR & LIDS

Tuesday, April 4, 2000
4:00 PM (reception following)
Room 35-225
LIDS Colloquium

Abstract

Problems involving moments of random variables arise naturally in many areas of mathematics, engineering, economics, and operations research. How do we obtain optimal bounds on the probability that a random variable belongs in a set, given some of its moments? How do we price financial derivatives without assuming any model for the underlying price dynamics, given only moments of the price of the underlying asset? How do we obtain stronger relaxations for stochastic optimization problems exploiting the knowledge that the decision variables are moments of random variables? How do we solve a partial differential equation without discretization? In this talk, we demonstrate that convex, and in particular semidefinite, optimization methods lead to interesting and often unexpected answers to these questions.

Short vita:

Dimitris Bertsimas is the Boeing Professor of Operations Research at MIT's Sloan School of Management. He has received a BS in Electrical Engineering and Computer Science at the National Technical University of Athens, Greece in 1985, a MS in Operations Research at MIT in 1987, and a Ph.D in Applied Mathematics and Operations Research at MIT in 1988. Since 1988, he has been with MIT's Sloan School of Management.

His research interests cover a broad range of areas in optimization, stochastic systems, statistics and financial economics. He is area editor for financial engineering in Operations Research. He has received several awards for his research including the Presidential Young Investigator award, the Erlang prize and the SIAM prize in optimization.