The next meeting of the seminar of the Department of Operations Research, Probability and Statistics will be held on October 17th, 2023, at 2:00 p.m. (UTC+3).

A talk on:

On an Infinite-Time Horizon Linear-Quadratic Game with Constrained Control

will be delivered by Boyan Stefanov.

Abstract. A linear-quadratic game on an infinite horizon for continuous and discrete-time systems is studied when the controls of the minimizing player are constrained. Our approach is based on the approximation of this game by a suitable finite-time horizon game. First, the existence of a saddle point equilibrium is proved for the unconstrained case. Next, it is established that there exists a delta-neighborhood of the origin in the state space where the control constraints are not active. Using this neighborhood, the original problem is reduced to a suitable finite-time horizon game. The main result is a sufficient condition for the existence of saddle point equilibrium. As an illustration, the approach is applied to a basic monetary policy model. The discrete case is also briefly discussed.