  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.
