  We study the optimal liquidation problems in target zone models using dynamic
programming methods. Such control problems allow for stochastic differential
equations with reflections and random coefficients. The value function is
characterized with a Neumann problem of backward stochastic partial
differential equations (BSPDEs) with singular terminal conditions. The
existence and the uniqueness of strong solution to such BSPDEs are addressed,
which in turn yields the optimal feedback control. In addition, the unique
existence of strong solution to Neumann problem of general semilinear BSPDEs in
finer functions space, a comparison theorem, and a new link between
forward-backward stochastic differential equations and BSPDE are proved as
well.
