Multi-period mean-variance optimal control of Markov jumps linear systems with multiplicative noise. / Controle ótimo multi-período de média-variância para sistemas lineares sujeitos a saltos Markovianos e ruídos multiplicativos.

AUTOR(ES)

Rodrigo Takashi Okimura

DATA DE PUBLICAÇÃO

2009

RESUMO

This thesis focuses on the stochastic optimal control problem of discrete-time linear systems subject to Markov jumps and multiplicative noise under three kinds of performance criterions related to the nal value of the expectation and variance of the output. In the first problem it is desired to minimize the nal variance of the output subject to a restriction on its nal expectation, in the second one it is desired to maximize the nal expectation of the output subject to a restriction on its nal variance, and in the third one it is considered a performance criterion composed by a linear combination of the nal variance and expectation of the output of the system. The optimal control strategies are obtained from a set of interconnected Riccati dierence equations and explicit sufficient conditions are presented for the existence of an optimal control strategy for these problems, generalizing previous results in the literature. Numerical simulations of investment portfolios and asset liabilities management models for pension funds with regime switching are presented.

ASSUNTO(S)

stochastic optimal control markov jump systems processos de markov sistemas discretos administração de carteiras multiplicative noise mean variance control controle estocástico

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