Optimal control of uncertain stochastic systems with Markovian switching and its applications to portfolio decisions

This paper first describes a class of uncertain stochastic control systems with Markovian switching, and derives an It\^o-Liu formula for Markov-modulated processes. And we characterize an optimal control law, which 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 also make an economic analysis through numerical examples.