Abstract: 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.

Abstract: Agent-based simulations may be a way to model human society behavior in decisions under risk. However, it is well known in economics that Expected Utility Theory (EUT) is flawed as a descriptive model. In fact, there are some models based on Prospect Theory (PT), that try to provide a better description. If people behave according to PT in finance environments, it is arguable that PT based agents may be a better choice for such environments. We investigate this idea, in a specific risky environment, financial market. We propose an architecture for PT-based agents. Due to some limitations of original PT, we use an extension of PT called Smooth Prospect Theory (SPT). We simulate artificial markets with PT and traditional (TRA) agents using historical data of many different assets over a period of twenty years. The results showed that SPT-based agents provided behavior closer to real market data than TRA agents in a statiscally significant way. It supports the idea that PT based agents may be a better pick to risky environments.

Abstract: This paper presents a graphical representation that fully depicts the price-time-volume dynamics in a Limit Order Book (LOB). Based on this pattern representation, a clustering technique is applied to predict market trends. The clustering technique is tested on information from the USD/COP market. Competitive trend prediction results were found, and a benchmark for future extensions was settled.

Abstract: Those empirical properties exhibited by high frequency financial data, such as time-varying intensities and self-exciting features, make it a challenge to model appropriately the dynamics associated with, for instance, order arrival. To capture the microscopic structures pertaining to limit order books, this paper focuses on modeling high frequency financial data using Hawkes processes. Specifically, the model with power-law kernels is compared with the counterpart with exponential kernels, on the goodness of fit to the empirical data, based on a number of proposed quantities for statistical tests. Based on one-trading-day data of one representative stock, it is shown that Hawkes processes with power-law kernels are able to reproduce the intensity of jumps in the price processes more accurately, which suggests that they could serve as a realistic model for high frequency data on the level of microstructure.