# On Parametric Optimal Execution and Machine Learning Surrogates

arXiv: https://arxiv.org/abs/2204.08581 · HTML: https://mlsanity.com/paper/2204.08581/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 54 references that are in the map.
- First posted on arXiv 18 Apr 2022.

## Builds on (most cited first, 11 of 11)

- [Recent Advances in Reinforcement Learning in Finance](https://mlsanity.com/paper/2112.04553/) (2021)
- [Deep Learning Approximation for Stochastic Control Problems](https://mlsanity.com/paper/1611.07422/) (2016)
- [Neural networks-based algorithms for stochastic control and PDEs in finance](https://mlsanity.com/paper/2101.08068/) (2021)
- [Learning a functional control for high-frequency finance](https://mlsanity.com/paper/2006.09611/) (2020)
- [Robust Markowitz mean-variance portfolio selection under ambiguous covariance matrix *](https://mlsanity.com/paper/1610.06805/) (2016)
- [Optimal Liquidation under Stochastic Liquidity](https://mlsanity.com/paper/1603.06498/) (2016)
- [Optimal Trade Execution with Instantaneous Price Impact and Stochastic Resilience](https://mlsanity.com/paper/1611.03435/) (2016)
- [Adaptive Robust Control Under Model Uncertainty](https://mlsanity.com/paper/1706.02227/) (2017)
- [Multi-dimensional Optimal Trade Execution under Stochastic Resilience](https://mlsanity.com/paper/1804.03896/) (2018)
- [Optimal trade execution in an order book model with stochastic liquidity parameters](https://mlsanity.com/paper/2006.05843/) (2020)
- [C`adl`ag semimartingale strategies for optimal trade execution in stochastic order book models](https://mlsanity.com/paper/2006.05863/) (2020)

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

- [A hierarchical resource-efficient deep policy gradient method for continuous-time optimal control problems](https://mlsanity.com/paper/2502.14141/) (2025)
- [Can Large Language Models Execute Parent Orders?](https://mlsanity.com/paper/2607.28410/) (2026)

## Abstract (arXiv)

We investigate optimal order execution problems in discrete time with instantaneous price impact and stochastic resilience. First, in the setting of linear transient price impact we derive a closed-form recursion for the optimal strategy, extending the deterministic results from Obizhaeva and Wang (J Financial Markets, 2013). Second, we develop a numerical algorithm based on dynamic programming and deep learning for the case of nonlinear transient price impact as proposed by Bouchaud et al. (Quant. Finance, 2004). Specifically, we utilize an actor-critic framework that constructs two neural-network (NN) surrogates for the value function and the feedback control. The flexible scalability of NN functional approximators enables parametric learning, i.e., incorporating several model or market parameters as part of the input space. Precise calibration of price impact, resilience, etc., is known to be extremely challenging and hence it is critical to understand sensitivity of the execution policy to these parameters. Our NN learner organically scales across multiple input dimensions and is shown to accurately approximate optimal strategies across a wide range of parameter configurations. We provide a fully reproducible Jupyter Notebook with our NN implementation, which is of independent pedagogical interest, demonstrating the ease of use of NN surrogates in (parametric) stochastic control problems.