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A Non-Markovian Liquidation Problem and Backward SPDEs with Singular Terminal Conditions (1309.0461v4)
Published 2 Sep 2013 in math.OC, math.PR, and q-fin.TR
Abstract: We establish 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 pre-specified. The analysis of such control problems is motivated by models of optimal portfolio liquidation.