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

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.

Keywords:

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

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work is supported in part by PolyU G-UA7U, and Hong Kong RGC grants 15224215 and 15255416.