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

Autor(es)

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

Afiliação do(s) autor(es)

^[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

• Tipo de documento: Artigo Científico
• Fonte: INTERNATIONAL JOURNAL OF SYSTEMS SCIENCE; v. 51, n. 10, p. 1825-1846, JUL 26 2020.
• Citações Web of Science: 0

Resumo

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)

• Processo FAPESP: 14/50279-4 - Brasil Research Centre for Gas Innovation
• Beneficiário: Julio Romano Meneghini
• Linha de fomento: Auxílio à Pesquisa - Programa Centros de Pesquisa em Engenharia
• Processo FAPESP: 14/50851-0 - INCT 2014: Instituto Nacional de Ciência e Tecnologia para Sistemas Autônomos Cooperativos Aplicados em Segurança e Meio Ambiente
• Beneficiário: Marco Henrique Terra
• Linha de fomento: Auxílio à Pesquisa - Temático