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.
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- Bertsimas, Dimitris & Lo, Andrew W., 1998. "Optimal control of execution costs," Journal of Financial Markets, Elsevier, vol. 1(1), pages 1-50, April.
- 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.
- Markus K. Brunnermeier & Lasse Heje Pedersen, 2004.
NBER Working Papers
10755, National Bureau of Economic Research, Inc.
- Markus K Brunnermeier & Lasse Heje Pederson, 2003. "Predatory Trading," FMG Discussion Papers dp441, Financial Markets Group.
- 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.
- 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.
- 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.
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