In this paper, we study a stochastic optimal control problem with 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 with respect to the uncertainty parameter of the
variational equation, which is characterized as forward-backward stochastic
differential equations. Second, using the linearization method and weak
convergence technique, we prove the necessary stochastic maximum principle and
show the sufficient condition of the stochastic optimal control. Finally, as an
application, a risk-minimizing portfolio selection problem is studied.
Meanwhile, the Lβ-solution and Lβ-estimate of stochastic
differential equations with regime switching are given for \b=2k with k∈N.Comment: 37 Page