  In this research, we develop a trading strategy for the discrete-time optimal
liquidation problem of large order trading with different market
microstructures in an illiquid market. In this framework, the flow of orders
can be viewed as a point process with stochastic intensity. We model the price
impact as a linear function of a self-exciting dynamic process. We formulate
the liquidation problem as a discrete-time Markov Decision Processes, where the
state process is a Piecewise Deterministic Markov Process (PDMP). The numerical
results indicate that an optimal trading strategy is dependent on
characteristics of the market microstructure. When no orders above certain
value come the optimal solution takes offers in the lower levels of the limit
order book in order to prevent not filling of orders and facing final inventory
costs.
