FIRST ORDER BSPDEs IN HIGHER DIMENSION FOR OPTIMAL CONTROL PROBLEMS - Dokuchaev, Nikolai (Society for Industrial and Applied Mathematics, 2017)
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.