A state-constrained differential game arising in optimal portfolio liquidation. (English) Zbl 1397.91561
Summary: 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.
Keywords:
optimal portfolio liquidation; optimal trade execution; illiquid markets; differential game with state constraintsReferences:
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