# 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…

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

- EconomicsAnnals of Operations Research
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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.…

### 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.

### 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).

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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.

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In financial markets, liquidity is not constant over time but exhibits strong seasonal patterns. In this paper, we consider a limit order book model that allows for time‐dependent, deterministic…

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In financial markets, liquidity changes randomly over time. We consider such random variations of the depth of the order book and evaluate their influence on optimal trade execution strategies. If…

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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…

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Abstract We study the problem of optimally liquidating a financial position in a discrete-time model with stochastic volatility and liquidity. We consider the three cases where the objective is to…

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It is proved that the solution to the liquidation problem can be approximated by the solutions to a sequence of unconstrained problems with increasing penalisation of open positions at the terminal time.

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This work builds on the resilience model proposed by Obizhaeva and Wang (2005) but allows for a general shape of the LOB defined via a given density function, and obtains a new closed-form representation for the optimal strategy of a risk-neutral investor.

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We give a complete solution to the problem of minimizing the expected liquidity costs in the presence of a general drift when the underlying market impact model has linear transient price impact with…