  We propose a framework to study the optimal liquidation strategy in a limit
order book for large-tick stocks, with 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 price move
directions. Our goal is to maximise the expected terminal wealth of an agent
who needs to liquidate her positions within a fixed time horizon. Assuming that
the agent trades (through sell limit order or/and sell market order) 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.
