Market microstructure has long classified trading activity by its informational role: an informed trader demands liquidity by trading in the direction of private information, while a market maker supplies liquidity by absorbing that order flow and earning the spread in compensation Kyle (1985); Glosten and Milgrom (1985). This classification is typically recovered from the data the classifier requires: signed order flow, quote revisions, or the sequential-trade structure of the market. The classification is harder to apply to an algorithmic strategy whose internal logic is unobservable. However, the signals or optimization problems generating the decisions of a typical quantitative fund are not visible, even though the trades and reported positions may be available. This paper shows that the liquidity role of such a strategy (consumer or provider) can be recovered from realized portfolio costs and trade decisions alone, without observing quotes, order flow, or any other microstructure-specific signal.

We investigate the mechanisms by which medium-frequency trading agents are adversely selected by opportunistic high-frequency traders. We use reinforcement learning (RL) within a Hawkes Limit Order Book (LOB) model in order to replicate the behaviours of high-frequency market makers. In contrast to the classical models with exogenous price impact assumptions, the Hawkes model accounts for endogenous price impact and other key properties of the market (Jain et al. 2024a). Given the real-world impracticalities of the market maker updating strategies for every event in the LOB, we formulate the high-frequency market making agent via an impulse control reinforcement learning framework (Jain et al. 2025). The RL used in the simulation utilises Proximal Policy Optimisation (PPO) and self-imitation learning. To replicate the adverse selection phenomenon, we test the RL agent trading against a medium frequency trader (MFT) executing a meta-order and demonstrate that, with training against the MFT meta-order execution agent, the RL market making agent learns to capitalise on the price drift induced by the meta-order. Recent empirical studies have shown that medium-frequency traders are increasingly subject to adverse selection by high-frequency trading agents. As high-frequency trading continues to proliferate across financial markets, the slippage costs incurred by medium-frequency traders are likely to increase over time. However, we do not observe that increased profits for the market making RL agent necessarily cause significantly increased slippages for the MFT agent.

Traditional methods for identifying impactful liquidity providers (LPs) in Concentrated Liquidity Market Makers (CLMMs) rely on broad measures, such as nominal capital size or surface-level activity, which often lead to inaccurate risk analysis. The SILS framework offers a significantly more detailed approach, characterizing LPs not just as capital holders but as dynamic systemic agents whose actions directly impact market stability. This represents a fundamental paradigm shift from the static, volume-based analysis to a dynamic, impact-focused understanding. This advanced approach uses on-chain event logs and smart contract execution traces to compute Exponential Time-Weighted Liquidity (ETWL) profiles and apply unsupervised anomaly detection. Most importantly, it defines an LP's functional importance through the Liquidity Stability Impact Score (LSIS), a counterfactual metric that measures the potential degradation of the market if the LP withdraws. This combined approach provides a more detailed and realistic characterization of an LP's impact, moving beyond the binary and often misleading classifications used by existing methods. This impact-focused and comprehensive approach enables SILS to accurately identify high-impact LPs-including those missed by traditional methods and supports essential applications like a protective oracle layer and actionable trader signals, thereby significantly enhancing DeFi ecosystem. The framework provides unprecedented transparency into the underlying liquidity structure and associated risks, effectively reducing the common false positives and uncovering critical false negatives found in traditional models. Therefore, SILS provides an effective mechanism for proactive risk management, transforming how DeFi protocols safeguard their ecosystems against asymmetric liquidity behavior.

We study operator learning in the context of linear propagator models for optimal order execution problems with transient price impact \`a la Bouchaud et al. (2004) and Gatheral (2010). Transient price impact persists and decays over time according to some propagator kernel. Specifically, we propose to use In-Context Operator Networks (ICON), a novel transformer-based neural network architecture introduced by Yang et al. (2023), which facilitates data-driven learning of operators by merging offline pre-training with an online few-shot prompting inference. First, we train ICON to learn the operator from various propagator models that maps the trading rate to the induced transient price impact. The inference step is then based on in-context prediction, where ICON is presented only with a few examples. We illustrate that ICON is capable of accurately inferring the underlying price impact model from the data prompts, even with propagator kernels not seen in the training data. In a second step, we employ the pre-trained ICON model provided with context as a surrogate operator in solving an optimal order execution problem via a neural network control policy, and demonstrate that the exact optimal execution strategies from Abi Jaber and Neuman (2022) for the models generating the context are correctly retrieved. Our introduced methodology is very general, offering a new approach to solving optimal stochastic control problems with unknown state dynamics, inferred data-efficiently from a limited number of examples by leveraging the few-shot and transfer learning capabilities of transformer networks.

We consider the dynamics and the interactions of multiple reinforcement learning optimal execution trading agents interacting with a reactive Agent-Based Model (ABM) of a financial market in event time. The model represents a market ecology with 3-trophic levels represented by: optimal execution learning agents, minimally intelligent liquidity takers, and fast electronic liquidity providers. The optimal execution agent classes include buying and selling agents that can either use a combination of limit orders and market orders, or only trade using market orders. The reward function explicitly balances trade execution slippage against the penalty of not executing the order timeously. This work demonstrates how multiple competing learning agents impact a minimally intelligent market simulation as functions of the number of agents, the size of agents' initial orders, and the state spaces used for learning. We use phase space plots to examine the dynamics of the ABM, when various specifications of learning agents are included. Further, we examine whether the inclusion of optimal execution agents that can learn is able to produce dynamics with the same complexity as empirical data. We find that the inclusion of optimal execution agents changes the stylised facts produced by ABM to conform more with empirical data, and are a necessary inclusion for ABMs investigating market micro-structure. However, including execution agents to chartist-fundamentalist-noise ABMs is insufficient to recover the complexity observed in empirical data.

We investigate optimal order execution problems in discrete time with instantaneous price impact and stochastic resilience. First, in the setting of linear transient price impact we derive a closed-form recursion for the optimal strategy, extending the deterministic results from Obizhaeva and Wang (J Financial Markets, 2013). Second, we develop a numerical algorithm based on dynamic programming and deep learning for the case of nonlinear transient price impact as proposed by Bouchaud et al. (Quant. Finance, 2004). Specifically, we utilize an actor-critic framework that constructs two neural-network (NN) surrogates for the value function and the feedback control. The flexible scalability of NN functional approximators enables parametric learning, i.e., incorporating several model or market parameters as part of the input space. Precise calibration of price impact, resilience, etc., is known to be extremely challenging and hence it is critical to understand sensitivity of the execution policy to these parameters. Our NN learner organically scales across multiple input dimensions and is shown to accurately approximate optimal strategies across a wide range of parameter configurations. We provide a fully reproducible Jupyter Notebook with our NN implementation, which is of independent pedagogical interest, demonstrating the ease of use of NN surrogates in (parametric) stochastic control problems.

We consider an offline learning problem for an agent who first estimates an unknown price impact kernel from a static dataset, and then designs strategies to liquidate a risky asset while creating transient price impact. We propose a novel approach for a nonparametric estimation of the propagator from a dataset containing correlated price trajectories, trading signals and metaorders. We quantify the accuracy of the estimated propagator using a metric which depends explicitly on the dataset. We show that a trader who tries to minimise her execution costs by using a greedy strategy purely based on the estimated propagator will encounter suboptimality due to so-called spurious correlation between the trading strategy and the estimator and due to intrinsic uncertainty resulting from a biased cost functional. By adopting an offline reinforcement learning approach, we introduce a pessimistic loss functional taking the uncertainty of the estimated propagator into account, with an optimiser which eliminates the spurious correlation, and derive an asymptotically optimal bound on the execution costs even without precise information on the true propagator. Numerical experiments are included to demonstrate the effectiveness of the proposed propagator estimator and the pessimistic trading strategy.

LOBs [22] are a fundamental market mechanism, which are used across a significant proportion of financial markets, including all major stock and derivatives exchanges. The benefits of having robust and realistic simulators for these markets are numerous. For example, they would allow the study of markets under different assumptions, and the investigation of AI techniques for training trading strategies. In a LOB market, matched orders result in trades and unmatched orders are stored in the two parts of the LOB, a collection of buy orders called bids (the bid book), and a collection of sell orders called asks (the ask book). Typically, each side of the LOB will contains hundreds of individual orders, and a real market would be updated at micro-second time resolution, driven by a wide range of market participants and facilitated by "high-frequency" market makers [45]. The development of AI-based automated trading strategies for LOB markets has been a growth area in recent years, both within academia and industry, spurred on in part by developments in deep learning and reinforcement learning. Two typical LOB trading problems that have been investigated are market making, where the goal is to provide liquidity to the market by being continually willing to buy and sell an asset (see, e.g., Spooner et al. [50], Jerome et al. [28], Gasperov and Kostanjcar 1

We consider a class of learning problems in which an agent liquidates a risky asset while creating both transient price impact driven by an unknown convolution propagator and linear temporary price impact with an unknown parameter. We characterize the trader's performance as maximization of a revenue-risk functional, where the trader also exploits available information on a price predicting signal. We present a trading algorithm that alternates between exploration and exploitation phases and achieves sublinear regrets with high probability. For the exploration phase we propose a novel approach for non-parametric estimation of the price impact kernel by observing only the visible price process and derive sharp bounds on the convergence rate, which are characterised by the singularity of the propagator. These kernel estimation methods extend existing methods from the area of Tikhonov regularisation for inverse problems and are of independent interest. The bound on the regret in the exploitation phase is obtained by deriving stability results for the optimizer and value function of the associated class of infinite-dimensional stochastic control problems. As a complementary result we propose a regression-based algorithm to estimate the conditional expectation of non-Markovian signals and derive its convergence rate.

In this paper we develop numerical pricing methodologies for European style Exchange Options written on a pair of correlated assets, in a market with finite liquidity. In contrast to the standard multi-asset Black-Scholes framework, trading in our market model has a direct impact on the asset's price. The price impact is incorporated into the dynamics of the first asset through a specific trading strategy, as in large trader liquidity model. Two-dimensional Milstein scheme is implemented to simulate the pair of assets prices. The option value is numerically estimated by Monte Carlo with the Margrabe option as controlled variate. Time complexity of these numerical schemes are included. Finally, we provide a deep learning framework to implement this model effectively in a production environment.