An approximate dynamic programming approach to risk sensitive control of execution costs

We study the problem of optimal execution within a dynamic programming framework. Given an exponential objective function, system variables which are normally distributed, and linear market dynamics, we derive a closed form solution for optimal trading trajectories. We show that a trader lacking private information has trajectories which are static in nature, whilst a trader with private information requires real time observations to execute optimally. We further show that Bellman's equations become increasingly complex to solve if either the market dynamics are nonlinear, or if additional constraints are added to the problem. As such, we propose an approximate dynamic program using linear programming which achieves near-optimality. The algorithm approximates the exponential objective function within a class of linear architectures, and takes advantage of a probabilistic constraint sampling scheme in order to terminate. The performance of the algorithm relies on the quality of the approximation, and as such we propose a set of heuristics for its efficient implementation.

Department dc:contributor.department

Massachusetts Institute of Technology. Dept. of Electrical Engineering and Computer Science.

Grantor dc:publisher

Massachusetts Institute of Technology

Year dc:date.issued

2009

Author dc:creator

• Jeria, David (David O. Jeria López)

Advisor dc:contributor.advisor

• Daniela Pucci de Farias.

• Electrical Engineering and Computer Science.

Statement dc:rights

• M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission.

Licence dc:rights.uri

• http://dspace.mit.edu/handle/1721.1/7582

Language dc:language.iso

eng

Handle dc:identifier.uri

http://hdl.handle.net/1721.1/55112

OAI identifier oai:identifier

oai:dspace.mit.edu:1721.1/55112