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

Optimal trade execution in an order book model with stochastic liquidity parameters