We study a constrained optimal control problem allowing for degenerate coefficients . The coefficients can be random and then the value function is described by a degenerate backward stochastic partial differential equation (BSPDE) with singular terminal condition. For this degenerate BSPDE, we prove the existence and uniqueness of the nonnegative solution .
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 .
R
allowing for degenerate coefficients
with possibly degenerate coefficients arising in models of optimal portfolio liquidation under market impact
R
and then
in which case
D
the
R
the nonnegative solution
a nonnegative solution. Our existence result requires a novel gradient estimate for degenerate BSPDEs