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We study the optimal liquidation problems in target zone models using dynamicprogramming methods. Such control problems allow for stochastic differentialequations with reflections and random coefficients. The value function ischaracterized with a Neumann problem of backward stochastic partialdifferential equations (BSPDEs) with singular terminal conditions. Theexistence and the uniqueness of strong solution to such BSPDEs are addressed,which in turn yields the optimal feedback control. In addition, the uniqueexistence of strong solution to Neumann problem of general semilinear BSPDEs infiner functions space, a comparison theorem, and a new link betweenforward-backward stochastic differential equations and BSPDE are proved aswell.

Optimal Liquidation in Target Zone Models and Neumann Problem of Backward SPDEs with Singular Terminal Condition