A Constrained Control Problem with Degenerate Coefficients and   Degenerate Backward SPDEs with Singular Terminal Condition
  We study a constrained optimal control problem with possibly degenerate coefficients arising in models of optimal portfolio liquidation under market impact. The coefficients can be random in which case the value function is described by a degenerate backward stochastic partial differential equation (BSPDE) with singular terminal condition. For this degenerate BSPDE, we prove existence and uniqueness of a nonnegative solution. Our existence result requires a novel gradient estimate for degenerate BSPDEs. 
Ulrich Horst and Jinniao Qiu and Qi Zhang
q-fin.MF math.PR