Optimal Liquidation under Stochastic Liquidity
Preprint
English
OPEN
Becherer, Dirk
;
Bilarev, Todor
;
Frentrup, Peter
(2016)

Related identifiers:
doi: 10.1007/s0078001703462

Subject:
Mathematics  Optimization and Control  Mathematics  Probability  Quantitative Finance  Trading and Market Microstructure  Quantitative Finance  Mathematical Finance  35R35, 49J40, 49L20, 60H30, 60J50, 60J55, 93E20, 91G80
We solve explicitly a twodimensional singular control problem of finite fuel type for 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 spirit of Predoiu, Shaikhet and Shreve (2011), is taken to be stochastic, being driven by own random noise. The optimal control is obtained as the local time of a diffusion process reflected at a nonconstant 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.

References
(3)
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