Optimal Execution considering Trading Signal and Execution Risk Simultaneously

• Main Authors: Yuan Cheng, Lan Wu
• Format: Article
• Language: English
• Published: Hindawi Limited 2021-01-01
• Series: Mathematical Problems in Engineering
• Online Access: http://dx.doi.org/10.1155/2021/5514413

In this paper, we study the optimal execution problem by considering the trading signal and the transaction risk simultaneously. We propose an optimal execution problem by taking into account the trading signal and the execution risk with the associated decay kernel function and the transient price impact function being of generalized forms. In particular, we solve the stochastic optimal control problems under the assumptions that the decay kernel function is the Dirac function and the transient price function is a linear function. We give the optimal executing strategies in state-feedback form and the Hamilton‐Jacobi‐Bellman equations that the corresponding value functions satisfy in the cases of a constant execution risk and a linear execution risk. We also demonstrate that our results can recover previous results when the process of the trading signal degenerates.