In an illiquid market as a result of a lack of counterparties and uncertainty about asset values, trading of assets is not being secured by the actual value. In this research, we develop an algorithmic trading strategy to deal with the discrete optimal liquidation problem of large order trading with different market microstructures in an illiquid market. In this market, order flow can be viewed as a Point process with stochastic arrival intensity. Interaction between price impact and price dynamics can be modeled as a dynamic optimization problem with price impact as a linear function of the 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) , which is a member of right continuous Markov Process family. We study the dynamics of a limit order book and its influence on the price dynamics and develop a stochastic model to retain the main statistical characteristics of limit order books in illiquid markets .
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 .
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and its influence on the price dynamics and develop a stochastic model to retain the main statistical characteristics of limit order books in illiquid markets
in order to prevent not filling of orders and facing final inventory costs