We investigate the use of Reinforcement Learning for the optimal execution of meta-orders, where the objective is to execute incrementally large orders while minimizing implementation shortfall and market impact over an extended period of time. Departing from traditional parametric approaches to price dynamics and impact modeling, we adopt a model-free, data-driven framework. Since policy optimization requires counterfactual feedback that historical data cannot provide, we employ the Queue-Reactive Model to generate realistic and tractable limit order book simulations that encompass transient price impact, and nonlinear and dynamic order flow responses. Methodologically, we train a Double Deep Q-Network agent on a state space comprising time, inventory, price, and depth variables, and evaluate its performance against established benchmarks. Numerical simulation results show that the agent learns a policy that is both strategic and tactical, adapting effectively to order book conditions and outperforming standard approaches across multiple training configurations. These findings provide strong evidence that model-free Reinforcement Learning can yield adaptive and robust solutions to the optimal execution problem.

Execution algorithms are vital to modern trading, they enable market participants to execute large orders while minimising market impact and transaction costs. As these algorithms grow more sophisticated, optimising them becomes increasingly challenging. In this work, we present a reinforcement learning (RL) framework for discovering optimal execution strategies, evaluated within a reactive agent-based market simulator. This simulator creates reactive order flow and allows us to decompose slippage into its constituent components: market impact and execution risk. We assess the RL agent's performance using the efficient frontier based on work by Almgren and Chriss, measuring its ability to balance risk and cost. Results show that the RL-derived strategies consistently outperform baselines and operate near the efficient frontier, demonstrating a strong ability to optimise for risk and impact. These findings highlight the potential of reinforcement learning as a powerful tool in the trader's toolkit.

Reinforcement Learning has emerged as a promising framework for developing adaptive and data-driven strategies, enabling market makers to optimize decision-making policies based on interactions with the limit order book environment. This paper explores the integration of a reinforcement learning agent in a market-making context, where the underlying market dynamics have been explicitly modeled to capture observed stylized facts of real markets, including clustered order arrival times, non-stationary spreads and return drifts, stochastic order quantities and price volatility. These mechanisms aim to enhance stability of the resulting control agent, and serve to incorporate domain-specific knowledge into the agent policy learning process. Our contributions include a practical implementation of a market making agent based on the Proximal-Policy Optimization (PPO) algorithm, alongside a comparative evaluation of the agent's performance under varying market conditions via a simulator-based environment. As evidenced by our analysis of the financial return and risk metrics when compared to a closed-form optimal solution, our results suggest that the reinforcement learning agent can effectively be used under non-stationary market conditions, and that the proposed simulator-based environment can serve as a valuable tool for training and pre-training reinforcement learning agents in market-making scenarios.

This paper presents a sophisticated multi-day turnover quantitative trading algorithm that integrates advanced deep learning techniques with comprehensive cross-sectional stock prediction for the Chinese A-share market. Our framework combines five interconnected modules: initial stock selection through deep cross-sectional prediction networks, opening signal distribution analysis using mixture models for arbitrage identification, market capitalization and liquidity-based dynamic position sizing, grid-search optimized profit-taking and stop-loss mechanisms, and multi-granularity volatility-based market timing models. The algorithm employs a novel approach to balance capital efficiency with risk management through adaptive holding periods and sophisticated entry/exit timing. Trained on comprehensive A-share data from 2010-2020 and rigorously backtested on 2021-2024 data, our method achieves remarkable performance with 15.2\% annualized returns, maximum drawdown constrained below 5\%, and a Sharpe ratio of 1.87. The strategy demonstrates exceptional scalability by maintaining 50-100 daily positions with a 9-day maximum holding period, incorporating dynamic profit-taking and stop-loss mechanisms that enhance capital turnover efficiency while preserving risk-adjusted returns. Our approach exhibits robust performance across various market regimes while maintaining high capital capacity suitable for institutional deployment.

Optimal execution in financial markets refers to the process of strategically transacting a large volume of assets over a period to achieve the best possible outcome by balancing the trade-off between market impact costs and timing or volatility risks. Traditional optimal execution strategies, such as static Almgren-Chriss models, often prove suboptimal in dynamic financial markets. This paper propose flowOE, a novel imitation learning framework based on flow matching models, to address these limitations. FlowOE learns from a diverse set of expert traditional strategies and adaptively selects the most suitable expert behavior for prevailing market conditions. A key innovation is the incorporation of a refining loss function during the imitation process, enabling flowOE not only to mimic but also to improve upon the learned expert actions. To the best of our knowledge, this work is the first to apply flow matching models in a stochastic optimal execution problem. Empirical evaluations across various market conditions demonstrate that flowOE significantly outperforms both the specifically calibrated expert models and other traditional benchmarks, achieving higher profits with reduced risk. These results underscore the practical applicability and potential of flowOE to enhance adaptive optimal execution.

Algorithmic trading in modern financial markets is widely acknowledged to exhibit strategic, game-theoretic behaviors whose complexity can be difficult to model. A recent series of papers (Chriss, 2024b,c,a, 2025) has made progress in the setting of trading for position building. Here parties wish to buy or sell a fixed number of shares in a fixed time period in the presence of both temporary and permanent market impact, resulting in exponentially large strategy spaces. While these papers primarily consider the existence and structural properties of equilibrium strategies, in this work we focus on the algorithmic aspects of the proposed model. We give an efficient algorithm for computing best responses, and show that while the temporary impact only setting yields a potential game, best response dynamics do not generally converge for the general setting, for which no fast algorithm for (Nash) equilibrium computation is known. This leads us to consider the broader notion of Coarse Correlated Equilibria (CCE), which we show can be computed efficiently via an implementation of Follow the Perturbed Leader (FTPL). We illustrate the model and our results with an experimental investigation, where FTPL exhibits interesting behavior in different regimes of the relative weighting between temporary and permanent market impact.

Transaction cost analysis is a fundamental aspect of financial trading and market impact is the main source of costs for medium and large sized investors [1]. Thus, estimating the potential impact and cost of a trading decision is important to assess its profitability. This is particularly true and challenging for metaorders, i.e. sequences of orders and trades executed gradually over a long time period and following a single investment decision. In fact, while there is a vast literature on estimating and modeling impact of individual trades (or orders) from public data, it is less clear if and how such models can be used to estimate the expected price trajectory of a metaorder and the associated impact cost. To this end, the industrial practice is to estimate market impact and the associated cost of a metaorder by using data on actual metaorder execution (for academic researches using this approach, see, for example, [2-5]). However this approach presents some pitfalls.

The Queue-Reactive model introduced by Huang et al. (2015) has become a standard tool for limit order book modeling, widely adopted by both researchers and practitioners for its simplicity and effectiveness. We present the Multidimensional Deep Queue-Reactive (MDQR) model, which extends this framework in three ways: it relaxes the assumption of queue independence, enriches the state space with market features, and models the distribution of order sizes. Through a neural network architecture, the model learns complex dependencies between different price levels and adapts to varying market conditions, while preserving the interpretable point-process foundation of the original framework. Using data from the Bund futures market, we show that MDQR captures key market properties including the square-root law of market impact, cross-queue correlations, and realistic order size patterns. The model demonstrates particular strength in reproducing both conditional and stationary distributions of order sizes, as well as various stylized facts of market microstructure. The model achieves this while maintaining the computational efficiency needed for practical applications such as strategy development through reinforcement learning or realistic backtesting.

This study investigates the development of an optimal execution strategy through reinforcement learning, aiming to determine the most effective approach for traders to buy and sell inventory within a limited time frame. Our proposed model leverages input features derived from the current state of the limit order book. To simulate this environment and overcome the limitations associated with relying on historical data, we utilize the multi-agent market simulator ABIDES, which provides a diverse range of depth levels within the limit order book. We present a custom MDP formulation followed by the results of our methodology and benchmark the performance against standard execution strategies. Our findings suggest that the reinforcement learning-based approach demonstrates significant potential.

Generative models aim to simulate realistic effects of various actions across different contexts, from text generation to visual effects. Despite efforts to build real-world simulators, leveraging generative models for virtual worlds, like financial markets, remains underexplored. In financial markets, generative models can simulate market effects of various behaviors, enabling interaction with market scenes and players, and training strategies without financial risk. This simulation relies on the finest structured data in financial market like orders thus building the finest realistic simulation. We propose Large Market Model (LMM), an order-level generative foundation model, for financial market simulation, akin to language modeling in the digital world. Our financial Market Simulation engine (MarS), powered by LMM, addresses the need for realistic, interactive and controllable order generation. Key objectives of this paper include evaluating LMM's scaling law in financial markets, assessing MarS's realism, balancing controlled generation with market impact, and demonstrating MarS's potential applications. We showcase MarS as a forecast tool, detection system, analysis platform, and agent training environment. Our contributions include pioneering a generative model for financial markets, designing MarS to meet domain-specific needs, and demonstrating MarS-based applications' industry potential.