The optimal execution of stock trades is a relevant and interesting problem as it is key in maximizing profits and reducing risks when investing in the stock market. In the case of large orders, the problem becomes even more complex as the impact of the order in the market has to be taken into account. The usual solution is to split large orders into a set of smaller suborders that must be executed within a prescribed time window. This leads to the problem of deciding when in the time window execute each suborder. There are popular ways of executing the trading of these split orders like those which try to track the "Time Weighted Average Price" and the "Volume Weighted Average Price", usually called TWAP and VWAP orders. This paper presents a strategy to optimize the splitting of large trade orders over a given time window. The strategy is based on the solution of an optimization problem that is applied following a receding horizon approach. This approach reduces the impact of prediction errors due to the uncertain market dynamics, by using new values of the price time series as they are available as time goes on. Suborder size constraints are taken into account in both market and limit orders. The strategy relies on price and traded volume forecast but it is independent of the prediction technique used. The performance index weighs not only the financial cost of the suborders, but also the impact on the market and the forecasting accuracy. A tailored optimization algorithm is proposed for efficiently solving the corresponding optimization problem. Most of the computations of the algorithm can be parallelized. Finally, the proposed approach has been tested through a case study composed by stocks of the Chinese A-share market.INDEX TERMS algorithmic trading, receding horizon optimization, large stock orders, limit orders, TWAP, VWAP.
In this paper, we extend the State-Space Kriging (SSK) modeling technique presented in a previous work by the authors in order to consider non-autonomous systems. SSK is a data-driven method that computes predictions as linear combinations of past outputs. To model the nonlinear dynamics of the system, we propose the Kernel-based State-Space Kriging (K-SSK), a new version of the SSK where kernel functions are used instead of resorting to considerations about the locality of the data. Also, a Kalman filter can be used to improve the predictions at each time step in the case of noisy measurements. A constrained tracking Nonlinear Model Predictive Control (NMPC) scheme using the black-box input-output model obtained by means of the K-SSK prediction method is proposed. Finally, a simulation example and a real experiment are provided in order to assess the performance of the proposed controller.
This work presents a new methodology to obtain probabilistic interval predictions of a dynamical system. The proposed strategy uses stored past system measurements to estimate the future evolution of the system. The method relies on the use of dissimilarity functions to estimate the conditional probability density function of the outputs. A family of empirical probability density functions, parameterized by means of two scalars, is introduced. It is shown that the proposed family encompasses the multivariable normal probability density function as a particular case. We show that the presented approach constitutes a generalization of classical estimation methods. A validation scheme is used to tune the two parameters on which the methodology relies. In order to prove the effectiveness of the presented methodology, some numerical examples and comparisons are provided.
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