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We establish existence, uniqueness and regularity of solution results for aclass of backward stochastic partial differential equations with singularterminal condition. The equation describes the value function of non-Markovianstochastic optimal control problem in which the terminal state of thecontrolled process is pre-specified. The analysis of such control problems ismotivated by models of optimal portfolio liquidation.

A Non-Markovian Liquidation Problem and Backward SPDEs with Singular Terminal Conditions