Smooth solutions to portfolio liquidation problems under price-sensitive market impact

Abstract

We consider the stochastic control problem of a financial trader that needs to unwind a large asset portfolio within a short period of time. The trader can simultaneously submit active orders to a primary market and passive orders to a dark pool. Our framework is flexible enough to allow for price-dependent impact functions describing the trading costs in the primary market and price-dependent adverse selection costs associated with dark pool trading. We prove that the value function can be characterized in terms of the unique smooth solution to a PDE with singular terminal value, establish its explicit asymptotic behavior at the terminal time, and give the optimal trading strategy in feedback form.

References in corpus (3)

• A Non-Markovian Liquidation Problem and Backward SPDEs with Singular Terminal Conditions
• An explicit solution of a non-linear quadratic constrained stochastic control problem with an application to optimal liquidation in dark pools with adverse selection
• BSDEs with singular terminal condition and control problems with constraints

Cited by in corpus (6)

• Optimal Liquidation under Stochastic Liquidity
• On finite population games of optimal trading
• Multi-dimensional Optimal Trade Execution under Stochastic Resilience
• A Constrained Control Problem with Degenerate Coefficients and Degenerate Backward SPDEs with Singular Terminal Condition
• Backward Stochastic Differential Equations with Nonmarkovian Singular Terminal Values
• A Note on Costs Minimization with Stochastic Target Constraints