A state-constrained differential game arising in optimal portfolio liquidation
We consider $n$ risk-averse agents who compete for liquidity in an Almgren--Chriss market impact model. Mathematically, this situation can be described by a Nash equilibrium for a certain linear-quadratic differential game with state constraints. The state constraints enter the problem as terminal boundary conditions for finite and infinite time horizons. We prove existence and uniqueness of Nash equilibria and give closed-form solutions in some special cases. We also analyze qualitative properties of the equilibrium strategies and provide corresponding financial interpretations.
References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Markus K. Brunnermeier & Lasse Heje Pedersen, 2005.
Journal of Finance,
American Finance Association, vol. 60(4), pages 1825-1863, 08.
- Markus K Brunnermeier & Lasse Heje Pederson, 2003. "Predatory Trading," FMG Discussion Papers dp441, Financial Markets Group.
- Markus K. Brunnermeier & Lasse Heje Pedersen, 2004. "Predatory Trading," NBER Working Papers 10755, National Bureau of Economic Research, Inc.
- Markus K. Brunnermeier & Lasse Heje Pederson, 2003. "Predatory trading," LSE Research Online Documents on Economics 24829, London School of Economics and Political Science, LSE Library.
- Brunnermeier, Markus K & Pedersen, Lasse Heje, 2004. "Predatory Trading," CEPR Discussion Papers 4639, C.E.P.R. Discussion Papers.
- Lasse H. Pedersen & Markus Brunnermeier, 2004. "Predatory Trading," Econometric Society 2004 North American Winter Meetings 425, Econometric Society.
- Bertsimas, Dimitris & Lo, Andrew W., 1998. "Optimal control of execution costs," Journal of Financial Markets, Elsevier, vol. 1(1), pages 1-50, April.
- Robert Almgren, 2003. "Optimal execution with nonlinear impact functions and trading-enhanced risk," Applied Mathematical Finance, Taylor & Francis Journals, vol. 10(1), pages 1-18.
- Charles-Albert Lehalle, 2013. "Market Microstructure Knowledge Needed for Controlling an Intra-Day Trading Process," Papers 1302.4592, arXiv.org.
- Bruce Ian Carlin & Miguel Sousa Lobo & S. Viswanathan, 2007. "Episodic Liquidity Crises: Cooperative and Predatory Trading," Journal of Finance, American Finance Association, vol. 62(5), pages 2235-2274, October.
- Alexander Schied & Torsten Schoneborn & Michael Tehranchi, 2010. "Optimal Basket Liquidation for CARA Investors is Deterministic," Applied Mathematical Finance, Taylor & Francis Journals, vol. 17(6), pages 471-489.
When requesting a correction, please mention this item's handle: RePEc:arx:papers:1312.7360. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (arXiv administrators)
If references are entirely missing, you can add them using this form.