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In this research, we develop a trading strategy for the discrete-time optimalliquidation problem of large order trading with different marketmicrostructures in an illiquid market. In this framework, the flow of orderscan be viewed as a point process with stochastic intensity. We model the priceimpact as a linear function of a self-exciting dynamic process. We formulatethe liquidation problem as a discrete-time Markov Decision Processes, where thestate process is a Piecewise Deterministic Markov Process (PDMP). The numericalresults indicate that an optimal trading strategy is dependent oncharacteristics of the market microstructure. When no orders above certainvalue come the optimal solution takes offers in the lower levels of the limitorder book in order to prevent not filling of orders and facing final inventorycosts.

Optimum Liquidation Problem Associated with the Poisson Cluster Process