Optimal Control of Uncertain Stochastic Systems with Markovian Switching and Its Applications to Portfolio Decisions
This article first describes a class of uncertain stochastic control systems with Markovian switching, and derives an Itô-Liu formula for Markov-modulated processes. We characterize an optimal control law, that satisfies the generalized Hamilton-Jacobi-Bellman (HJB) equation with
Markovian switching. Then, by using the generalized HJB equation, we deduce the optimal consumption and portfolio policies under uncertain stochastic financial markets with Markovian switching. Finally, for constant relative risk-aversion (CRRA) felicity functions, we explicitly obtain the
optimal consumption and portfolio policies. Moreover, we make an economic analysis through numerical examples.
Keywords: HJB equations; Markovian switching; generalized Itô-Liu formula; optimal consumption and portfolio; optimal control of uncertain stochastic systems; uncertain random variables
Document Type: Research Article
Affiliations: School of Mathematics and Physics, Anhui Polytechnic University, Wuhu, Anhui, P.R. China
Publication date: 02 January 2014
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