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.

In recent years, the popularity of artificial intelligence has surged due to its widespread application in various fields. The financial sector has harnessed its advantages for multiple purposes, including the development of automated trading systems designed to interact autonomously with markets to pursue different aims. In this work, we focus on the possibility of recognizing and leveraging intraday price patterns in the Foreign Exchange market, known for its extensive liquidity and flexibility. Our approach involves the implementation of a Reinforcement Learning algorithm called Fitted Natural Actor-Critic. This algorithm allows the training of an agent capable of effectively trading by means of continuous actions, which enable the possibility of executing orders with variable trading sizes. This feature is instrumental to realistically model transaction costs, as they typically depend on the order size. Furthermore, it facilitates the integration of risk-averse approaches to induce the agent to adopt more conservative behavior. The proposed approaches have been empirically validated on EUR-USD historical data.

In this paper, we show how $K$-nearest neighbor ($K$-NN) resampling, an off-policy evaluation method proposed in \cite{giegrich2023k}, can be applied to simulate limit order book (LOB) markets and how it can be used to evaluate and calibrate trading strategies. Using historical LOB data, we demonstrate that our simulation method is capable of recreating realistic LOB dynamics and that synthetic trading within the simulation leads to a market impact in line with the corresponding literature. Compared to other statistical LOB simulation methods, our algorithm has theoretical convergence guarantees under general conditions, does not require optimization, is easy to implement and computationally efficient. Furthermore, we show that in a benchmark comparison our method outperforms a deep learning-based algorithm for several key statistics. In the context of a LOB with pro-rata type matching, we demonstrate how our algorithm can calibrate the size of limit orders for a liquidation strategy. Finally, we describe how $K$-NN resampling can be modified for choices of higher dimensional state spaces.

Investors and regulators can greatly benefit from a realistic market simulator that enables them to anticipate the consequences of their decisions in real markets. However, traditional rule-based market simulators often fall short in accurately capturing the dynamic behavior of market participants, particularly in response to external market impact events or changes in the behavior of other participants. In this study, we explore an agent-based simulation framework employing reinforcement learning (RL) agents. We present the implementation details of these RL agents and demonstrate that the simulated market exhibits realistic stylized facts observed in real-world markets. Furthermore, we investigate the behavior of RL agents when confronted with external market impacts, such as a flash crash. Our findings shed light on the effectiveness and adaptability of RL-based agents within the simulation, offering insights into their response to significant market events.

In this paper, we introduce Max Markov Chain (MMC), a novel representation for a useful subset of High-order Markov Chains (HMCs) with sparse correlations among the states. MMC is parsimony while retaining the expressiveness of HMCs. Even though parameter optimization is generally intractable as with HMC approximate models, it has an analytical solution, better sample efficiency, and the desired spatial and computational advantages over HMCs and approximate HMCs. Simultaneously, efficient approximate solutions exist for this type of chains as we show empirically, which allow MMCs to scale to large domains where HMCs and approximate HMCs would struggle to perform. We compare MMC with HMC, first-order Markov chain, and an approximate HMC model in synthetic domains with various data types to demonstrate that MMC is a valuable alternative for modeling stochastic processes and has many potential applications.

People often ask me about the impact of 3D printing on jobs. Will the technology be a job creator or destroyer? The short answer is, it will take more jobs than it makes -- and 3D printing is not alone. Technology will eventually make work obsolete. Our big problems are going to be figuring out how to survive the transition, then figuring out what to do with all that free time. About 10 years ago, inventor, futurist and now Director of Engineering at Google Ray Kurzweil famously embraced the concept of "the singularity" -- that moment in time when machine intelligence surpasses our own. Kurzweil predicted the singularity would occur by 2045, and man and machine would become inseparable.