On linear, degenerate backward stochastic partial differential equations

In this paper we study the well-posedness and regularity of the adapted sol utions to a class of linear, degenerate backward stochastic partial differe ntial equations (BSPDE, for short). We establish new a priori estimates for the adapted solutions to BSPDEs in a general setting, based on which the e xistence, uniqueness, and regularity of adapted solutions are obtained. Als o, we prove some comparison theorems and discuss their possible application s in mathematical finance. Mathematics Subject Classification (1991): 60H15 , 35R60, 34F05, 93E20.