# Càdlàg semimartingale strategies for optimal trade execution in stochastic order book models

@article{Ackermann2020CdlgSS, title={C{\`a}dl{\`a}g semimartingale strategies for optimal trade execution in stochastic order book models}, author={Julia Ackermann and Thomas Kruse and Mikhail Urusov}, journal={Finance and Stochastics}, year={2020}, volume={25}, pages={757 - 810} }

We analyse an optimal trade execution problem in a financial market with stochastic liquidity. To this end, we set up a limit order book model in continuous time. Both order book depth and resilience are allowed to evolve randomly in time. We allow trading in both directions and for càdlàg semimartingales as execution strategies. We derive a quadratic BSDE that under appropriate assumptions characterises minimal execution costs, and we identify conditions under which an optimal execution…

## 10 Citations

### Optimal Trade Execution in an Order Book Model with Stochastic Liquidity Parameters

- EconomicsSIAM J. Financial Math.
- 2021

A limit order book model is set up in which both order book depth and resilience evolve randomly in time, and an explicit recursion that, under certain structural assumptions, characterizes minimal execution costs is derived.

### Optimal trade execution under small market impact and portfolio liquidation with semimartingale strategies

- Mathematics
- 2021

We consider an optimal liquidation problem with instantaneous price impact and stochastic resilience for small instantaneous impact factors. Within our modelling framework, the optimal portfolio…

### A Mean-Field Control Problem of Optimal Portfolio Liquidation with Semimartingale Strategies

- Mathematics
- 2022

We consider a mean-ﬁeld control problem with c`adl`ag semimartingale strategies arising in portfolio liquidation models with transient market impact and self-exciting order ﬂow. We show that the…

### Small impact analysis in stochastically illiquid markets ∗ – Convergence of optimal portfolio processes –

- Mathematics
- 2021

We consider an optimal liquidation problem with instantaneous price impact and stochastic resilience for small instantaneous impact factors. Within our modelling framework, the optimal portfolio…

### On effects of negative resilience on optimal trade execution in stochastic order books

- Economics
- 2021

Most of the existing literature on optimal trade execution in limit order book models assumes that resilience is positive. But negative resilience also has a natural interpretation, as it models…

### Reducing Obizhaeva-Wang type trade execution problems to LQ stochastic control problems

- Mathematics
- 2022

We start with a stochastic control problem where the control process is of finite variation (possibly with jumps) and acts as integrator both in the state dynamics and in the target functional.…

### On Parametric Optimal Execution and Machine Learning Surrogates

- Computer ScienceArXiv
- 2022

A closed-form recursion for the optimal strategy is derived and a fully reproducible Jupyter Notebook is provided with the NN implementation, demonstrating the ease of use of NN surrogates in (parametric) stochastic control problems.

### On the Dynamic Cumulative Past Quantile Entropy Ordering

- MathematicsSymmetry
- 2021

A quantile version of DCPE is obtained, termed as the dynamic cumulative past quantile entropy (DCPQE).

### Optimal Liquidation Through a Limit Order Book: A Neural Network and Simulation Approach

- Computer ScienceMethodology and Computing in Applied Probability
- 2023

A learning algorithm based on simulation and neural networks to solve a stochastic optimal control problem with a large state space using dynamic programming and outperforms the most common optimal liquidation models in the literature by a significant amount.

### Self-exciting price impact via negative resilience in stochastic order books

- EconomicsAnnals of Operations Research
- 2022

Most of the existing literature on optimal trade execution in limit order book models assumes that resilience is positive. But negative resilience also has a natural interpretation, as it models…

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