Optimal Liquidation in a Level-I Limit Order Book for Large Tick Stocks

We propose a framework to study the optimal liquidation strategy in a limit order book for large-tick stocks, with the spread equal to one tick. All order book events (market orders, limit orders and cancellations) occur according to independent Poisson processes, with parameters depending on the most recent price move direction. Our goal is to maximise the expected terminal wealth of an agent who needs to liquidate her positions within a fixed time horizon. By assuming that the agent trades (through both limit and market orders) only when the price moves, we model her liquidation procedure as a semi-Markov decision process, and compute the semi-Markov kernel using Laplace method in the language of queueing theory. The optimal liquidation policy is then solved by dynamic programming, and illustrated numerically