# C`adl`ag semimartingale strategies for optimal trade execution in stochastic order book models

arXiv: https://arxiv.org/abs/2006.05863 · HTML: https://mlsanity.com/paper/2006.05863/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Jun 2020.

## Built on by (most cited first, 1 of 1)

- [On Parametric Optimal Execution and Machine Learning Surrogates](https://mlsanity.com/paper/2204.08581/) (2022)

## Abstract (arXiv)

We analyze 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 for trading in both directions and for c`adl`ag semimartingales as execution strategies. We derive a quadratic BSDE that under appropriate assumptions characterizes minimal execution costs and identify conditions under which an optimal execution strategy exists. We also investigate qualitative aspects of optimal strategies such as, e.g., appearance of strategies with infinite variation or existence of block trades and discuss connections with the discrete-time formulation of the problem. Our findings are illustrated in several examples.