quantitative analysts

Abstract: The limit order book (LOB) records outstanding buy and sell orders across multiple price levels. Its state evolves over time across market side, price level, and order attribute, naturally forming a multiway structure. However, existing LOB models typically flatten these dimensions into a matrix model, thus obscuring the existing structural relationships. Starting from first principles and the market-microstructure intuition of the LOB, we design TensorLOB to operate entirely in the tensor domain. TensorLOB uses mode-wise tensor contractions for feature extraction and directly contracts the learned representation with low-rank class-weight tensors for prediction, retaining the distinct roles of time, side, level, and attribute modes. Experiments on the FI-2010 benchmark show that TensorLOB achieves the highest accuracy, recall, and F1 score across all four evaluated horizons. This proof of concept highlights the potential of high-dimensional modelling of multi-way latent information intrinsic to financial markets, which has so far been largely overlooked.

Abstract: Artificial intelligence (AI) in finance has evolved from statistical learning and machine learning for structured prediction, through deep learning and foundation models for representation learning, language understanding, and reasoning, to retrieval-augmented generation for knowledge-grounded reasoning and agentic AI for autonomous planning and execution. In this paper, we examine how researchers and practitioners can select and apply AI methods in finance. We first show that the major paradigms of financial AI address fundamentally different classes of problems, rather than forming a strict hierarchy of capability. We then review the current state of research on AI in finance and trace how these paradigms have reshaped financial data, financial tasks, decision support, and human-AI collaboration. Building on this, we propose practical guidelines for matching AI paradigms to task characteristics, and show that more advanced models, such as foundation models or autonomous agents, are not universally superior. We conclude by outlining open challenges for researchers and practitioners working toward reliable financial AI.

Abstract: We consider the problem of estimating the background intensity of a Hawkes process when the triggering mechanism is known, treating the background as an unknown finite positive measure with a regular density. We propose a likelihood-based variational approach based on the Wasserstein-Fisher-Rao geometry. In this setting, the relevant first variations are naturally distribution-valued and therefore fall outside the classical gradient-flow formulation. We develop a distributional framework for the resulting dynamics and give them a finite-dimensional meaning through projections onto statistical manifolds. We identify the true background as the unique zero of a limiting generalized gradient and, under suitable stability, compactness, integrability and approximation conditions, establish a conditional consistency theorem for measurable estimators satisfying the empirical projected equations on events whose probabilities tend to one. Finally, we specialize the construction to Gaussian-mixture manifolds and obtain an explicit finite-dimensional scheme.

Abstract: Building a world model requires a state representation useful for planning and decision-making---potentially over tasks unknown at training time. In the context of financial markets, planning and decision-making may require a model to reason about market-wide conditions, asset-specific expected returns, liquidity, volatility, and cross-asset relationships. Yet financial representation learning has largely been evaluated on individual predictive tasks, oftentimes on a single time period using comparatively narrow datasets. We address this through three primary contributions. First, we introduce Market-1T, a dataset containing nearly one trillion observations across U.S. equities from 2008 to 2025 at 1 Hz resolution. Second, we develop and implement a rigorous evaluation protocol. Third, we conduct a systematic large-scale study of financial representation learning, comparing 18 encoder-training strategies across nearly two decades of market regimes. We evaluate learned representations both by their predictive utility on common finance tasks and through probes of latent structure. We find that encoders with similar predictive performance can organize market state very differently. Collectively, we establish a foundation for training and evaluating financial market representations in support of world models such as DINO-WM, V-JEPA 2, and LeWM.

Abstract: In finance, interpreting machine learning predictions is essential, yet the numerical outputs of explainable AI can be difficult for non-experts to understand. While large language models (LLMs) can translate these outputs into natural language, they may produce errors when inferring numerical changes and feature relations. We propose an LLM narrative framework for cross-sectional stock return prediction that combines temporal Shapley additive explanations (SHAP) evidence with historical regime analogs. Temporal evidence tracks changes in the normalized global SHAP importance of an XGBoost model over six months. Historical analogs are past periods with similar changes in SHAP importance, their model performance and subsequent market returns are provided as comparative context. Using this framework, we conduct a controlled study of progressive reasoning externalization, sequentially providing raw SHAP sequences, deterministic temporal descriptors, and feature relations. Each generated claim is verified against provenance-linked evidence. Across Qwen3, externalizing numerical and relational reasoning improved evidence faithfulness as well as temporal and relational accuracy. Evidence faithfulness increased from 0.696 to 0.996 for Qwen3-32B-Instruct. While historical analogs did not improve structured automatic faithfulness, they received higher human-rated usefulness scores. These results suggest that externalizing verifiable reasoning enhances narrative faithfulness and that historical context adds interpretive value.

Abstract: In many settings involving stochastic differential equations, including in diffusion based generative AI, our aim is to accurately generate samples from a terminal distribution. Typically, this is done by generating i.i.d. samples of diffusion paths. Given a fixed simulation budget, a reasonable way to gain efficiency may be to instead generate a tree of paths through appropriately split partial paths. This suggests improved performance, but one worries about the injected dependence. In this paper, we study this issue comprehensively. With Kolmogorov-Smirnov distance as a measure of accuracy, we identify the limiting errors of the associated empirical distributions as the simulation budget increases to infinity. We characterize a splitting strategy motivated by a corresponding asymptotic optimization problem. The theoretical results bring out the elegant underlying structure in the problem. Practical implementation involves two phases, an initial estimation phase and a final inference phase. Overall, we observe a 10-25% improvement in mean error over i.i.d. samples in many settings. In an exploratory CIFAR-10 study, our method reduces the maximum mean discrepancy by 8-13%.