  In this paper, we establish a general stochastic maximum principle for
optimal control for systems described by a continuous-time Markov
regime-switching stochastic recursive utilities model. The control domain is
postulated not to be convex, and the diffusion terms depend on control
variables. To this end, we first study a kind of classical forward stochastic
optimal control problems. Afterwards, based on previous results, we introduce
two groups of new first and second-order adjoint equations. The corresponding
variational equations for forward-backward stochastic differential equations
are derived. In particular, the generator in the maximum principle contains
solutions of second-order adjoint equation which is novel. Some interesting
examples are concluded as well.
