  We analyze an optimal trade execution problem in a financial market with
stochastic liquidity. To this end we set up a limit order book model in which
both order book depth and resilience evolve randomly in time. Trading is
allowed in both directions and at discrete points in time. We derive an
explicit recursion that, under certain structural assumptions, characterizes
minimal execution costs. We also discuss several qualitative aspects of optimal
strategies, such as existence of profitable round trips or closing the position
in one go, and compare our findings with the literature.
