# Optimal Liquidation under Stochastic Liquidity

arXiv: https://arxiv.org/abs/1603.06498 · HTML: https://mlsanity.com/paper/1603.06498/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Mar 2016.

## Built on by (most cited first, 2 of 2)

- [From Deep Learning to LLMs: A survey of AI in Quantitative Investment](https://mlsanity.com/paper/2503.21422/) (2025)
- [On Parametric Optimal Execution and Machine Learning Surrogates](https://mlsanity.com/paper/2204.08581/) (2022)

## Abstract (arXiv)

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.