A discrete-time mean-field stochastic linear-quadratic optimal control problem with financial application

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Abstract

This paper is concerned with a discrete-time mean-field stochastic linear-quadratic optimal control problem arising from financial application. Through matrix dynamical optimisation method, a group of linear feedback controls is investigated. The problem is then reformulated as an operator stochastic linear-quadratic optimal control problem by a sequence of bounded linear operators over Hilbert space, the optimal control with six algebraic Riccati difference equations is obtained by backward induction. The two above approaches are proved to be coincided by the classical method of completing the square. Finally, after discussing the solution of the problem under multidimensional noises, a financial application example is given.
Original languageEnglish
Pages (from-to)175-189
Number of pages15
JournalInternational Journal of Control
Volume94
Issue number1
DOIs
Publication statusPublished - Jan 2021

Keywords

  • Mean-field theory
  • Riccati difference equation
  • stochastic linear-quadratic optimal control problem

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Computer Science Applications

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