Transient Linear Price Impact and Fredholm Integral Equations
Mathematical Finance, Forthcoming
30 Pages Posted: 5 Jan 2010 Last revised: 3 May 2011
There are 2 versions of this paper
Transient Linear Price Impact and Fredholm Integral Equations
Transient Linear Price Impact and Fredholm Integral Equations
Date Written: May 30, 2010
Abstract
We consider the linear-impact case in the continuous-time market impact model with transient price impact proposed by Gatheral (2008). In this model, the absence of price manipulation in the sense of Huberman and Stanzl (2004) can easily be characterized by means of Bochner's theorem. This allows us to study the problem of minimizing the expected liquidation costs of an asset position under constraints on the trading times. We prove that optimal strategies can be characterized as measure-valued solutions of a generalized Fredholm integral equation of the first kind and analyze several explicit examples. We also prove theorems on the existence and nonexistence of optimal strategies. We show in particular that optimal strategies always exist and are nonalternating between buy and sell trades when price impact decays as a convex function of time. This is based on and extends a recent result by Alfonsi, Schied, and Slynko (2009) on the nonexistence of transaction-triggered price manipulation. We also prove some qualitative properties of optimal strategies and provide explicit expressions for the optimal strategy in several special cases of interest.
Keywords: Transient price impact, market impact model, optimal order execution, price manipulation, transaction-triggered price manipulation, Fredholm integral equation
Suggested Citation: Suggested Citation
Do you have a job opening that you would like to promote on SSRN?
Recommended Papers
-
Optimal Trading Strategy and Supply/Demand Dynamics
By Anna A. Obizhaeva and Jiang Wang
-
Optimal Trading Strategy and Supply/Demand Dynamics
By Anna A. Obizhaeva and Jiang Wang
-
Optimal Trading Strategy and Supply/Demand Dynamics
By Anna A. Obizhaeva and Jiang Wang
-
Optimal Execution Strategies in Limit Order Books with General Shape Functions
By Aurélien Alfonsi, Antje Fruth, ...
-
By Olaf Korn and Alexander Kempf
-
Quasi-Arbitrage and Price Manipulation
By Gur Huberman and Werner Stanzl
-
Fluctuations and Response in Financial Markets: The Subtle Nature of 'Random' Price Changes
By Jean-philippe Bouchaud, Yuval Gefen, ...
-
By Gur Huberman and Werner Stanzl
-
How Markets Slowly Digest Changes in Supply and Demand
By Jean-philippe Bouchaud, J. Doyne Farmer, ...
-
No-Dynamic-Arbitrage and Market Impact
By Jim Gatheral