  We study a multi-dimensional optimal execution problem in illiquid markets
with both instantaneous and persistent price impact and stochastic resilience.
In our model the value function can be described by a multi-dimensional
backward stochastic Riccati differential equations (BSRDE) with a singular
terminal condition in one component. We prove the existence of a solution to
the BSRDE system and characterise both the value function and the optimal
strategy in terms of that solution. We prove that the solution to the
liquidation problem can be approximated by the solutions to a sequence of
unconstrained problems with increasing penalisation of open positions at the
terminal time.
