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Optimal liquidation under stochastic liquidity


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.

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    Subject(s)
    s Stochastic liquidity
    Transient price impact
    Optimal liquidation
    Stochastic volume effect
    Singular control
    Finite-fuel problem
    Free boundary
    Inverse local time
    Elastic reflection
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