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# Joint Probability/Statistics Seminar and Math Finance Colloquium: Turnpike Properties for Stochastic Linear-Quadratic Optimal Control Problems

Friday, April 7, 2023 3:30pm to 4:30pm

About this Event

3620 South Vermont Avenue, Los Angeles, CA 90089

**Jiongmin Yong, University of Central Florida**

[in-person]

or

Zoom Meeting: https://usc.zoom.us/j/91559216343?pwd=N1Yrb3E3WGE2Uk1UZDcwWU4rTlVPdz09

Meeting ID: 915 5921 6343

Passcode: 402421

Abstract: 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.

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