The present paper is focused on the solution of optimal control problems such as optimal acquisition, optimal liquidation, and market making in relation to the high-frequency trading market. We have modeled optimal control problems with the price approximated by the diffusion process for the...

We apply the well-known CUSUM, the Girshick-Rubin, the Graversen-Peskir- Shiryaev and an improved alteration of the Brodsky-Darkovsky algorithm as trading strategies involving only mutually exclusive long positions in cash and the DAX at Xetra intraday auction prices. We select optimal pairs of...

Modern Algorithmic Trading ("Algo") allows institutional investors and traders to liquidate or establish big security positions in a fully automated or low-touch manner. Most existing academic or industrial Algos focus on how to "slice" a big parent order into smaller child orders over a given...