Please use this identifier to cite or link to this item: https://hdl.handle.net/10419/315062 
Year of Publication: 
2024
Citation: 
[Journal:] Finance and Stochastics [ISSN:] 1432-1122 [Volume:] 28 [Issue:] 3 [Publisher:] Springer Berlin Heidelberg [Place:] Berlin/Heidelberg [Year:] 2024 [Pages:] 813-863
Publisher: 
Springer Berlin Heidelberg, Berlin/Heidelberg
Abstract: 
Abstract We start with a stochastic control problem where the control process is of finite variation (possibly with jumps) and acts as integrator both in the state dynamics and in the target functional. Problems of such type arise in the stream of literature on optimal trade execution pioneered by Obizhaeva and Wang (J. Financ. Mark. 16:1–32, 2013 ) (models with finite resilience). We consider a general framework where the price impact and the resilience are stochastic processes. Both are allowed to have diffusive components. First we continuously extend the problem from processes of finite variation to progressively measurable processes. Then we reduce the extended problem to a linear–quadratic (LQ) stochastic control problem. Using the well-developed theory on LQ problems, we describe the solution to the obtained LQ one and translate it back to the solution for the (extended) initial trade execution problem. Finally, we illustrate our results by several examples. Among other things, the examples discuss the Obizhaeva–Wang model with random (terminal and moving) targets, the necessity to extend the initial trade execution problem to a reasonably large class of progressively measurable processes (even going beyond semimartingales), and the effects of diffusive components in the price impact process and/or the resilience process.
Subjects: 
Optimal trade execution
Stochastic price impact
Stochastic resilience
Finite-variation stochastic control
Continuous extension of cost functional
Progressively measurable execution strategy
Linear–quadratic stochastic control
Backward stochastic differential equation
Persistent Identifier of the first edition: 
Additional Information: 
C02;G10;G11
Creative Commons License: 
cc-by Logo
Document Type: 
Article
Document Version: 
Published Version
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