Mean-Field Stochastic Linear Quadratic Optimal Control Problems: Closed-Loop Solvability

Xun Li, Jingrui Sun, Jiongmin Yong

Research output: Journal article publicationJournal articleAcademic researchpeer-review

41 Citations (Scopus)

Abstract

An optimal control problem is studied for a linear mean-field stochastic differential equation with a quadratic cost functional. The coefficients and the weighting matrices in the cost functional are all assumed to be deterministic. Closed-loop strategies are introduced, which require to be independent of initial states; and such a nature makes it very useful and convenient in applications. In this paper, the existence of an optimal closed-loop strategy for the system (also called the closed-loop solvability of the problem) is characterized by the existence of a regular solution to the coupled two (generalized) Riccati equations, together with some constraints on the adapted solution to a linear backward stochastic differential equation and a linear terminal value problem of an ordinary differential equation.

Original languageEnglish
Article number2
JournalProbability, Uncertainty and Quantitative Risk
Volume1
Issue number1
DOIs
Publication statusPublished - Jan 2016

Keywords

  • Closed-loop solvability
  • Linear quadratic optimal control
  • Mean-field stochastic differential equation
  • Regular solution
  • Riccati equation

ASJC Scopus subject areas

  • Statistics and Probability
  • Applied Mathematics
  • Statistics, Probability and Uncertainty

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