A Constrained Control Problem with Degenerate Coefficients and Degenerate Backward SPDEs with Singular Terminal Condition
We study a constrained optimal control problem allowing for degenerate coefficients. The coefficients can be random and then the value function is described by a degenerate backward stochastic partial differential equation (BSPDE) with singular terminal condition. For this degenerate BSPDE, we prove the existence and uniqueness of the nonnegative solution.