Dynamic Portfolio Execution and Information Relaxations

Posted: 10 Sep 2012 Last revised: 10 Jun 2014

Martin Haugh

Columbia University - Department of Industrial Engineering and Operations Research (IEOR)

Chun Wang

Columbia University - Department of Industrial Engineering and Operations Research (IEOR)

Date Written: January 18, 2014

Abstract

We consider a portfolio execution problem where a possibly risk-averse agent needs to trade a fixed number of shares in multiple stocks over a short time horizon. Our price dynamics can capture linear but stochastic temporary and permanent price impacts as well as stochastic volatility. In general it's not possible to solve even numerically for the optimal policy in this model, however, and so we must instead search for good sub-optimal policies. Our principal policy is a variant of an open-loop feedback control (OLFC) policy and we show how the corresponding OLFC value function may be used to construct good primal and dual bounds on the optimal value function. The dual bound is constructed using the recently developed duality methods based on information relaxations. One of the contributions of this paper is the identification of sufficient conditions to guarantee convexity, and hence tractability, of the associated dual problem instances. That said, we do not claim that the only plausible models are those where all dual problem instances are convex. We also show that it is straightforward to include a non-linear temporary price impact as well as return predictability in our model. We demonstrate numerically that good dual bounds can be computed quickly even when nested Monte-Carlo simulations are required to estimate the so-called dual penalties. These results suggest that the dual methodology can be applied in many models where closed-form expressions for the dual penalties cannot be computed.

Keywords: portfolio execution, sub-optimal control, martingale duality

JEL Classification: C61, C63, G11

Suggested Citation

Haugh, Martin and Wang, Chun, Dynamic Portfolio Execution and Information Relaxations (January 18, 2014). Available at SSRN: https://ssrn.com/abstract=2144517 or http://dx.doi.org/10.2139/ssrn.2144517

Martin Haugh (Contact Author)

Columbia University - Department of Industrial Engineering and Operations Research (IEOR) ( email )

331 S.W. Mudd Building
500 West 120th Street
New York, NY 10027
United States

Chun Wang

Columbia University - Department of Industrial Engineering and Operations Research (IEOR) ( email )

331 S.W. Mudd Building
500 West 120th Street
New York, NY 10027
United States

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