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Keywords:

  • market impact model;
  • optimal order execution;
  • limit order book;
  • resilience;
  • time-varying liquidity;
  • price manipulation;
  • transaction-triggered price manipulation

In financial markets, liquidity is not constant over time but exhibits strong seasonal patterns. In this paper, we consider a limit order book model that allows for time-dependent, deterministic depth and resilience of the book and determine optimal portfolio liquidation strategies. In a first model variant, we propose a trading-dependent spread that increases when market orders are matched against the order book. In this model, no price manipulation occurs and the optimal strategy is of the wait region/buy region type often encountered in singular control problems. In a second model, we assume that there is no spread in the order book. Under this assumption, we find that price manipulation can occur, depending on the model parameters. Even in the absence of classical price manipulation, there may be transaction triggered price manipulation. In specific cases, we can state the optimal strategy in closed form.