Self-exciting price impact via negative resilience in stochastic order books - Julia Ackermann; Thomas Kruse; Mikhail Urusov (Annals of Operations Research, 2022)
Most of the existing literature on optimal trade execution in limit order book models assumes that resilience is positive. But negative resilience also has a natural interpretation, as it models self-exciting behaviour of the price impact, where trading activities of the large investor stimulate other market participants to trade in the same direction. In the paper we discuss several new qualitative effects on optimal trade execution that arise when we allow resilience to take negative values. We do this in a framework where both market depth and resilience are stochastic processes.
Keywords: 000; Optimal trade execution; Limit order book; Stochastic market depth; Stochastic resilience; Negative resilience; Quadratic BSDE; Infinite-variation execution strategy; Semimartingale execution strategy