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.