Optimal execution with multiplicative price impact

Guo, Xin and Zervos, Mihail (2015) Optimal execution with multiplicative price impact. SIAM Journal on Financial Mathematics, 6 (1). pp. 281-306. ISSN 1945-497X

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Abstract

We consider the so-called optimal execution problem in algorithmic trading, which is the problem faced by an investor who has a large number of stock shares to sell over a given time horizon and whose actions have an impact on the stock price. In particular, we develop and study a price model that presents the stochastic dynamics of a geometric Brownian motion and incorporates a log-linear effect of the investor’s transactions. We then formulate the optimal execution problem as a degenerate singular stochastic control problem. Using both analytic and probabilistic techniques, we establish simple conditions for the market to allow for no arbitrage or price manipulation and develop a detailed characterization of the value function and the optimal strategy. In particular, we derive an explicit solution to the problem if the time horizon is infinite.

Item Type:	Article
Official URL:	http://epubs.siam.org/loi/sjfmbj
Additional Information:	© 2015 Society for Industrial and Applied Mathematics
Library of Congress subject classification:	Q Science > QA Mathematics
Sets:	Departments > Mathematics
Date Deposited:	18 Feb 2016 16:57
URL:	http://eprints.lse.ac.uk/65409/

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