A Pre-Trade Algorithmic Trading Model under Given Volume Measures and Generic Price Dynamics (GVM-GPD)

Jackie Shen

Papers from arXiv.org

Abstract: We make several improvements to the mean-variance framework for optimal pre-trade algorithmic execution, by working with volume measures and generic price dynamics. Volume measures are the continuum analogies for discrete volume profiles commonly implemented in the execution industry. Execution then becomes an absolutely continuous measure over such a measure space, and its Radon-Nikodym derivative is commonly known as the Participation of Volume (PoV) function. The four impact cost components are all consistently built upon the PoV function. Some novel efforts are made for these linear impact models by having market signals more properly expressed. For the opportunistic cost, we are able to go beyond the conventional Brownian-type motions. By working directly with the auto-covariances of the price dynamics, we remove the Markovian restriction associated with Brownians and thus allow potential memory effects in the price dynamics. In combination, the final execution model becomes a constrained quadratic programming problem in infinite-dimensional Hilbert spaces. Important linear constraints such as participation capping are all permissible. Uniqueness and existence of optimal solutions are established via the theory of positive compact operators in Hilbert spaces. Several typical numerical examples explain both the behavior and versatility of the model.

Date: 2013-09, Revised 2013-09
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://arxiv.org/pdf/1309.5046 Latest version (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:arx:papers:1309.5046

Access Statistics for this paper

More papers in Papers from arXiv.org
Bibliographic data for series maintained by arXiv administrators ().