A mean-field formulation for the mean-variance control of discrete-time linear systems with multiplicative noises

Author(s)

Barbieri, Fabio ^[1] ; Costa, Oswaldo L. V. ^[2]

Affiliation

^[1] Univ Sao Paulo, Escola Politecn, Dept Telecommun & Control Engn, Sao Paulo - Brazil

^[2] Univ Sao Paulo, Escola Politecn, Dept Telecommun & Control Engn, Control Grp, Sao Paulo - Brazil

• Document type: Journal article
• Source: INTERNATIONAL JOURNAL OF SYSTEMS SCIENCE; v. 51, n. 10, p. 1825-1846, JUL 26 2020.
• Web of Science Citations: 0

Abstract

This paper considers the stochastic optimal control of a multi-period mean-variance trade-off performance criterion with and without constraints for discrete-time linear systems subject to multiplicative noises. We adopt a mean-field approach to tackle the problem and obtain a solution for the unconstrained case in terms of a Riccati-like difference equation. From this general result, we obtain a sufficient condition for a closed-form solution for one of the constrained problems considered in the paper. When particularised to the portfolio selection problem, we show that our results retrieve some of the results available in the literature. We conclude the paper by illustrating the obtained optimal controls with a multi-period portfolio selection problem where we minimise the sum of the mean-variance trade-off costs of a portfolio against a benchmark along the time. (AU)

• FAPESP's process: 14/50279-4 - Brasil Research Centre for Gas Innovation
• Grantee: Julio Romano Meneghini
• Support Opportunities: Research Grants - Applied Research Centers Program
• FAPESP's process: 14/50851-0 - INCT 2014: National Institute of Science and Technology for Cooperative Autonomous Systems Applied in Security and Environment
• Grantee: Marco Henrique Terra
• Support Opportunities: Research Projects - Thematic Grants