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

Abstract

We establish the existence, uniqueness, and regularity of solution results for a class of backward stochastic partial differential equations with singular terminal condition. The equation describes the value function of non-Markovian stochastic optimal control problem in which the terminal state of the controlled process is prespecified. The analysis of such control problems is motivated by models of optimal portfolio liquidation.

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