For deterministic optimal control problems in very large time horizons (either finite dimensional or infinite dimensional), under proper conditions, the optimal pair will stay near a solution of a proper static optimization problem. Such a phenomenon is called the “turnpike” property. The proper static optimization problem usually is the one with the objective function being the running cost rate function and with the constraint being the equilibria of the vector field of the state equation. However, for stochastic problems, mimicking the idea of the deterministic problems will lead to some incorrect conclusions. In this talk, we will look at stochastic linear-quadratic optimal control problem in large duration. We will correctly formulate the proper static optimization problem and establish the turnpike properties of the corresponding stochastic linear-quadratic problem.

Biography

Jiongmin Yong is a professor of mathematics at University of Central Florida. He obtained his BS degree in 1982 at Fudan University, and his PhD degree in 1986 at Purdue University, under supervision of L. D. Berkovitz. Professor Yong’s research interests include control theory, stochastic differential/integral equations, and mathematical finance. He was teaching in Fudan University during 1988 —2003, promoted to a full professor in 1991, and became a Cheung Kong Professor in 2000. He was the chair of Department of Mathematics at Fudan University during 2000—2003. Since 2003, he has been a professor at University of Central Florida. Professor Yong was/is an associate editor of several journals, including SIAM Journal on Control and Optimization, ESAIM: Control, Optimization and Calculus of Variations, and Mathematical Control and Related Topics. He won a number of honors, including Su Buqing Mathematical Prize, SAIG/SCT Best SICON Paper Prize, and was invited to deliver a 45-minute talk at 2014 ICM.