FIRST ORDER BSPDEs IN HIGHER DIMENSION FOR OPTIMAL CONTROL PROBLEMS
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This paper studies the first order backward stochastic partial differential equations suggested earlier for a case of multidimensional state domain with a boundary. These equations represent analogues of Hamilton--Jacobi--Bellman equations and allow one 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 modeling.
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