Modeling the dynamics of financial Limit Order Books (LOB) at the message level is challenging due to irregular event timing, rapid regime shifts, and the reactions of high-frequency traders to visible order flow. Previous LOB models require cumbersome data representations and lack adaptability outside their original tasks, leading us to introduce LOBERT, a general-purpose encoder-only foundation model for LOB data suitable for downstream fine-tuning. LOBERT adapts the original BERT architecture for LOB data by using a novel tokenization scheme that treats complete multi-dimensional messages as single tokens while retaining continuous representations of price, volume, and time. With these methods, LOBERT achieves leading performance in tasks such as predicting mid-price movements and next messages, while reducing the required context length compared to previous methods.

Large language models (LLMs) exhibit complementary strengths across domains and come with varying inference costs, motivating the design of multi-agent LLM systems where specialized models collaborate efficiently. Existing approaches predominantly rely on decentralized frameworks, which invoke multiple LLMs for every input and thus lead to substantial and uncontrolled inference costs. In this work, we introduce a centralized multi-LLM framework, where a controller LLM selectively coordinates a pool of expert models in a cost-efficient and cost-controllable manner. We formulate this coordination problem as reinforcement learning with dual objectives: maximizing task performance while minimizing the overall inference cost. In addition, we expect the multi-agent system to have adapted behavior with different budget conditions during inference. To this end, we propose CoRL, a reinforcement learning framework that optimizes the performance cost trade-off in a controllable multi-budget setting. Experiments on four diverse benchmarks demonstrate that CoRL enables a single system to surpass the best expert LLM under high-budget settings, while maintaining strong performance in more economical low-budget modes, highlighting the effectiveness of centralized coordination for scalable and cost-efficient multi-agent LLM systems.

Modeling limit order books (LOBs) dynamics is a fundamental problem in market microstructure research. In particular, generating high-dimensional volume snapshots with strong temporal and liquidity-dependent patterns remains a challenging task, despite recent work exploring the application of Generative Adversarial Networks to LOBs. In this work, we propose a conditional \textbf{Diff}usion model for the generation of future LOB \textbf{Volume} snapshots (\textbf{DiffVolume}). We evaluate our model across three axes: (1) \textit{Realism}, where we show that DiffVolume, conditioned on past volume history and time of day, better reproduces statistical properties such as marginal distribution, spatial correlation, and autocorrelation decay; (2) \textit{Counterfactual generation}, allowing for controllable generation under hypothetical liquidity scenarios by additionally conditioning on a target future liquidity profile; and (3) \textit{Downstream prediction}, where we show that the synthetic counterfactual data from our model improves the performance of future liquidity forecasting models. Together, these results suggest that DiffVolume provides a powerful and flexible framework for realistic and controllable LOB volume generation.

This study examines how indoor and outdoor aesthetics, streetscapes, and neighborhood features shape customer satisfaction at eating and dining establishments (EDEs) across different urban contexts, varying in car dependency, in Washington, DC. Using review photos and street view images, computer vision models quantified perceived safety and visual appeal. Ordinal logistic regression analyzed their effects on Yelp ratings. Findings reveal that both indoor and outdoor environments significantly impact EDE ratings, while streetscape quality's influence diminishes in car-dependent areas. The study highlights the need for context-sensitive planning that integrates indoor and outdoor factors to enhance customer experiences in diverse settings.

The latency of the exchanges in Market Making (MM) is inevitable due to hardware limitations, system processing times, delays in receiving data from exchanges, the time required for order transmission to reach the market, etc. Existing reinforcement learning (RL) methods for Market Making (MM) overlook the impact of these latency, which can lead to unintended order cancellations due to price discrepancies between decision and execution times and result in undesired inventory accumulation, exposing MM traders to increased market risk. Therefore, these methods cannot be applied in real MM scenarios. To address these issues, we first build a realistic MM environment with random delays of 30-100 milliseconds for order placement and market information reception, and implement a batch matching mechanism that collects orders within every 500 milliseconds before matching them all at once, simulating the batch auction mechanisms adopted by some exchanges. Then, we propose Relaver, an RL-based method for MM to tackle the latency and inventory risk issues. The three main contributions of Relaver are: i) we introduce an augmented state-action space that incorporates order hold time alongside price and volume, enabling Relaver to optimize execution strategies under latency constraints and time-priority matching mechanisms, ii) we leverage dynamic programming (DP) to guide the exploration of RL training for better policies, iii) we train a market trend predictor, which can guide the agent to intelligently adjust the inventory to reduce the risk. Extensive experiments and ablation studies on four real-world datasets demonstrate that \textsc{Relaver} significantly improves the performance of state-of-the-art RL-based MM strategies across multiple metrics.

The Limit Order Book (LOB), the mostly fundamental data of the financial market, provides a fine-grained view of market dynamics while poses significant challenges in dealing with the esteemed deep models due to its strong autocorrelation, cross-feature constrains, and feature scale disparity. Existing approaches often tightly couple representation learning with specific downstream tasks in an end-to-end manner, failed to analyze the learned representations individually and explicitly, limiting their reusability and generalization. This paper conducts the first systematic comparative study of LOB representation learning, aiming to identify the effective way of extracting transferable, compact features that capture essential LOB properties. We introduce LOBench, a standardized benchmark with real China A-share market data, offering curated datasets, unified preprocessing, consistent evaluation metrics, and strong baselines. Extensive experiments validate the sufficiency and necessity of LOB representations for various downstream tasks and highlight their advantages over both the traditional task-specific end-to-end models and the advanced representation learning models for general time series. Our work establishes a reproducible framework and provides clear guidelines for future research. Datasets and code will be publicly available at https://github.com/financial-simulation-lab/LOBench.

While financial data presents one of the most challenging and interesting sequence modelling tasks due to high noise, heavy tails, and strategic interactions, progress in this area has been hindered by the lack of consensus on quantitative evaluation paradigms. To address this, we present LOB-Bench, a benchmark, implemented in python, designed to evaluate the quality and realism of generative message-by-order data for limit order books (LOB) in the LOBSTER format. Our framework measures distributional differences in conditional and unconditional statistics between generated and real LOB data, supporting flexible multivariate statistical evaluation. The benchmark also includes features commonly used LOB statistics such as spread, order book volumes, order imbalance, and message inter-arrival times, along with scores from a trained discriminator network. Lastly, LOB-Bench contains "market impact metrics", i.e. the cross-correlations and price response functions for specific events in the data. We benchmark generative autoregressive state-space models, a (C)GAN, as well as a parametric LOB model and find that the autoregressive GenAI approach beats traditional model classes.

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.

Market making (MM) has attracted significant attention in financial trading owing to its essential function in ensuring market liquidity. With strong capabilities in sequential decision-making, Reinforcement Learning (RL) technology has achieved remarkable success in quantitative trading. Nonetheless, most existing RL-based MM methods focus on optimizing single-price level strategies which fail at frequent order cancellations and loss of queue priority. Strategies involving multiple price levels align better with actual trading scenarios. However, given the complexity that multi-price level strategies involves a comprehensive trading action space, the challenge of effectively training profitable RL agents for MM persists. Inspired by the efficient workflow of professional human market makers, we propose Imitative Market Maker (IMM), a novel RL framework leveraging both knowledge from suboptimal signal-based experts and direct policy interactions to develop multi-price level MM strategies efficiently. The framework start with introducing effective state and action representations adept at encoding information about multi-price level orders. Furthermore, IMM integrates a representation learning unit capable of capturing both short- and long-term market trends to mitigate adverse selection risk. Subsequently, IMM formulates an expert strategy based on signals and trains the agent through the integration of RL and imitation learning techniques, leading to efficient learning. Extensive experimental results on four real-world market datasets demonstrate that IMM outperforms current RL-based market making strategies in terms of several financial criteria. The findings of the ablation study substantiate the effectiveness of the model components.

High-frequency quantitative investment is a crucial aspect of stock investment. Notably, order flow data plays a critical role as it provides the most detailed level of information among high-frequency trading data, including comprehensive data from the order book and transaction records at the tick level. The order flow data is extremely valuable for market analysis as it equips traders with essential insights for making informed decisions. However, extracting and effectively utilizing order flow data present challenges due to the large volume of data involved and the limitations of traditional factor mining techniques, which are primarily designed for coarser-level stock data. To address these challenges, we propose a novel framework that aims to effectively extract essential factors from order flow data for diverse downstream tasks across different granularities and scenarios. Our method consists of a Context Encoder and an Factor Extractor. The Context Encoder learns an embedding for the current order flow data segment's context by considering both the expected and actual market state. In addition, the Factor Extractor uses unsupervised learning methods to select such important signals that are most distinct from the majority within the given context. The extracted factors are then utilized for downstream tasks. In empirical studies, our proposed framework efficiently handles an entire year of stock order flow data across diverse scenarios, offering a broader range of applications compared to existing tick-level approaches that are limited to only a few days of stock data. We demonstrate that our method extracts superior factors from order flow data, enabling significant improvement for stock trend prediction and order execution tasks at the second and minute level.