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Backward stochastic partial differential equations of parabolic type inbounded domains are studied in the setting where the coercivity condition isnot necessary satisfied and the equation can be degenerate. Some generalizedsolutions based on the representation theorem are suggested. In addition toproblems with a standard Cauchy condition at the terminal time, problems withspecial non-local boundary conditions are considered. These non-localconditions connect the terminal value of the solution with a functional overthe entire past solution. Uniqueness, solvability and regularity results areobtained. Some applications to portfolio selection problem are considered.

Degenerate backward SPDEs in domains: non-local boundary conditions and applications to finance