We solve explicitly a two-dimensional singular control problem of finite fuel type in infinite time horizon. The problem stems from the optimal liquidation of an asset position in a financial market with multiplicative price impact with stochastic resilience . The optimal control is obtained as  a diffusion process reflected at a non-constant free boundary. To solve the  variational inequality and prove optimality, we show new results of independent interest on constructive approximations and Laplace transforms of the inverse local times for diffusions reflected at elastic boundaries.
We solve explicitly a two-dimensional 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 inter-temporal 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 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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in
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price impact with stochastic resilience
and transient price impact. Liquidity is stochastic in that the volume effect process, which determines the inter-temporal resilience of the market in spirit of Predoiu, Shaikhet and Shreve (2011), is taken to be stochastic, being driven by own random noise
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the local time of
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HJB
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show new results of independent interest on constructive approximations and
need a combination of probabilistic arguments and calculus of variations methods, involving
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the