Optimal Liquidation under Stochastic Liquidity
arXiv:1603.06498 · doi:10.1007/s00780-017-0346-2
Abstract
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.
arXiv commentAppeared in Finance and Stochastics as "online first". The final publication is available at link.springer.com
References in corpus (5)
- Martingale proofs of many-server heavy-traffic limits for Markovian queues
- Optimal Trade Execution with Instantaneous Price Impact and Stochastic Resilience
- Smooth solutions to portfolio liquidation problems under price-sensitive market impact
- Optimal Asset Liquidation with Multiplicative Transient Price Impact
- Incorporating Signals into Optimal Trading
Cited by in corpus (7)
- Stability for gains from large investors' strategies in M1/J1 topologies
- Optimal Asset Liquidation with Multiplicative Transient Price Impact
- Extended Mean Field Games with Singular Controls
- Understanding the dual formulation for the hedging of path-dependent options with price impact
- Second order stochastic target problems with generalized market impact
- Optimal installation of renewable electricity sources: the case of Italy
- Approximating diffusion reflections at elastic boundaries