Optimal liquidation under stochastic liquidity

Dirk Becherer (), Todor Bilarev () and Peter Frentrup ()
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Dirk Becherer: Humboldt-Universität zu Berlin
Todor Bilarev: Humboldt-Universität zu Berlin
Peter Frentrup: Humboldt-Universität zu Berlin

Finance and Stochastics, 2018, vol. 22, issue 1, No 2, 39-68

Abstract: Abstract We solve explicitly a two-dimensional singular control problem of finite fuel type for an infinite time horizon. The problem stems from the optimal liquidation of an asset position in a financial market with multiplicative and transient price impact. Liquidity is stochastic in that the volume effect process, which determines the intertemporal resilience of the market in the spirit of Predoiu et al. (SIAM J. Financ. Math. 2:183–212, 2011), is taken to be stochastic, being driven by its own random noise. The optimal control is obtained as the local time of a diffusion process reflected at a non-constant free boundary. To solve the HJB variational inequality and prove optimality, we need a combination of probabilistic arguments and calculus of variations methods, involving Laplace transforms of inverse local times for diffusions reflected at elastic boundaries.

Keywords: Stochastic liquidity; Transient price impact; Optimal liquidation; Stochastic volume effect; Singular control; Finite-fuel problem; Free boundary; Inverse local time; Elastic reflection; 35R35; 49J40; 49L20; 60H30; 60J50; 60J55; 93E20; 91G80 (search for similar items in EconPapers)
JEL-codes: C02 C61 D99 G12 G33 (search for similar items in EconPapers)
Date: 2018
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (19)

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DOI: 10.1007/s00780-017-0346-2

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