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A STATE‐CONSTRAINED DIFFERENTIAL GAME ARISING IN OPTIMAL PORTFOLIO LIQUIDATION
Author(s) -
Schied Alexander,
Zhang Tao
Publication year - 2017
Publication title -
mathematical finance
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.98
H-Index - 81
eISSN - 1467-9965
pISSN - 0960-1627
DOI - 10.1111/mafi.12108
Subject(s) - mathematical economics , uniqueness , nash equilibrium , differential game , portfolio , state (computer science) , differential (mechanical device) , mathematics , mathematical optimization , economics , finance , mathematical analysis , algorithm , engineering , aerospace engineering
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.