Optimal Execution with a Price Limiter

RISK, July 2014

11 Pages Posted: 13 Jan 2013 Last revised: 27 Apr 2015

See all articles by Sebastian Jaimungal

Sebastian Jaimungal

University of Toronto - Department of Statistics

Damir Kinzebulatov

The Fields Institute for Mathematical Sciences

Date Written: January 12, 2013

Abstract

Agents often wish to limit the price they pay for an asset. If they are acquiring a large number of shares, they must balance the risk of trading slowly (to limit price impact) with the risk of future uncertainty in prices. Here, we address the optimal acquisition problem for an agent who is unwilling to pay more than a specified price for an asset while they are subject to market impact and price uncertainty. The problem is posed as an optimal stochastic control and we provide an analytical closed form solution for the perpetual case as well as a dimensionally reduced PDE for the general case. The optimal speed of trading is found to no longer be deterministic and instead slows when maturity and the price barrier approaches. Moreover, we demonstrate that a price limiter constraint significantly reduces the conditional tail expectation of the securities costs.

Keywords: Optimal Execution, Optimal Liquidation, Stochastic Control, Conditional Tail Expectation, Limit Order Book

JEL Classification: C6, C61, C73, G12

Suggested Citation

Jaimungal, Sebastian and Kinzebulatov, Damir, Optimal Execution with a Price Limiter (January 12, 2013). RISK, July 2014, Available at SSRN: https://ssrn.com/abstract=2199889 or http://dx.doi.org/10.2139/ssrn.2199889

Sebastian Jaimungal (Contact Author)

University of Toronto - Department of Statistics ( email )

100 St. George St.
Toronto, Ontario M5S 3G3
Canada

HOME PAGE: http://http:/sebastian.statistics.utoronto.ca

Damir Kinzebulatov

The Fields Institute for Mathematical Sciences ( email )

222 College Street, Second Floor
Toronto, Ontario M5T 3J1
Canada

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