  The paper studies the First Order BSPDEs (Backward Stochastic Partial
Differential Equations) suggested earlier for a case of multidimensional state
domain with a boundary. These equations represent analogs of
Hamilton-Jacobi-Bellman equations and allow to construct the value function for
stochastic optimal control problems with unspecified dynamics where the
underlying processes do not necessarily satisfy stochastic differential
equations of a known kind with a given structure. The problems considered arise
in financial modelling.
