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

Autor(es)

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

Afiliação do(s) autor(es)

^[1] Univ Sao Paulo, Escola Politecn, Dept Engn Telecomunicacoes & Controle, BR-05508010 Sao Paulo - Brazil

• Tipo de documento: Artigo Científico
• Fonte: IET Control Theory and Applications; v. 14, n. 17, p. 2600-2612, NOV 26 2020.
• Citações Web of Science: 0

Resumo

This study considers the infinite-horizon stochastic optimal control of a discounted and long-run average costs under a mean-variance trade-off performance criterion for discrete-time linear systems subject to multiplicative noises. The authors adopt a mean-field approach to tackle the problem and get an optimal control solution in terms of a set of two generalised coupled algebraic Riccati equations (GCAREs). Then, they establish sufficient conditions for the existence of the maximal solution and necessary and sufficient conditions for the existence of the mean-square stabilising solution to the GCARE. From this solution, they derive optimal control policies to the related discounted and long-run average cost problems. A numerical example illustrates the obtained results for the multi-period portfolio selection problem in which it is desired to minimise the sum of the mean-variance trade-off costs of a portfolio against a benchmark along the time. (AU)

• 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
• 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