  In this paper, we study a stochastic optimal control problem for a Markovian
regime switching system, where the coefficients of the state equation and the
cost functional are uncertain. First, we obtain the variational inequality by
showing the continuity of solutions to variational equations with respect to
the uncertainty parameter $\theta$. Second, using the linearization and weak
convergence techniques, we prove the necessary stochastic maximum principle of
the stochastic optimal control. Finally, as an application, a risk-minimizing
portfolio selection problem is studied. In addition, $L^\beta$-solutions and
$L^\beta$-estimates of stochastic differential equations with regime switching
are given for $\beta=2k$ with $k\in \mathbb{N}$.
