Optimal liquidation problem in illiquid markets

•Proposing an analytical solution for the optimal liquidation problem in an illiquid market.•Applying trading boundaries built-in on the market depth to adjust the speed of trading.•Expressing the distribution of the limit order book analytically.•Modelling dynamics of incoming orders and measuring the price impact using Hawkes Processes.•Investigating the dependency of optimal trading strategies on market characteristics. In this research, we develop a trading strategy for the optimal liquidation problem of large-order trading, with different market microstructures, in an illiquid market. We formulate the liquidation problem as a discrete-time Markov decision process. In this market, the flow of liquidity events can be viewed as a point process with stochastic intensity. Based on this fact, we model the price impact as a linear function of a self-exciting dynamic process. Our trading algorithm is designed in such a way that when no favourite orders arrive in the Limit Order Book (LOB), the optimal solution takes offers from the lower levels of the LOB. This solution might contradict conventional optimal execution methods, which only trade with the best available limit orders; however, our findings show that the proposed strategy may reduce final inventory costs by preventing orders not being filled at earlier trading times. Furthermore, the results indicate that an optimal trading strategy is dependent on characteristics of the market microstructure.