This paper investigates theoretical and methodological foundations for stochastic optimal control (SOC) in discrete time. We start formulating the control problem in a general dynamic programming framework, introducing the mathematical structure needed for a detailed convergence analysis. The associate value function is estimated through a sequence of approximations combining nonparametric regression methods and Monte Carlo subsampling. The regression step is performed within reproducing kernel Hilbert spaces (RKHSs), exploiting the classical KRR algorithm, while Monte Carlo sampling methods are introduced to estimate the continuation value. To assess the accuracy of our value function estimator, we propose a natural error decomposition and rigorously control the resulting error terms at each time step. We then analyze how this error propagates backward in time-from maturity to the initial stage-a relatively underexplored aspect of the SOC literature. Finally, we illustrate how our analysis naturally applies to a key financial application: the pricing of American options.

Recent advances in machine learning have shown promising results for financial prediction using large, over-parameterized models. This paper provides theoretical foundations and empirical validation for understanding when and how these methods achieve predictive success. I examine two key aspects of high-dimensional learning in finance. First, I prove that within-sample standardization in Random Fourier Features implementations fundamentally alters the underlying Gaussian kernel approximation, replacing shift-invariant kernels with training-set dependent alternatives. Second, I establish information-theoretic lower bounds that identify when reliable learning is impossible no matter how sophisticated the estimator. A detailed quantitative calibration of the polynomial lower bound shows that with typical parameter choices, e.g., 12,000 features, 12 monthly observations, and R-square 2-3%, the required sample size to escape the bound exceeds 25-30 years of data--well beyond any rolling-window actually used. Thus, observed out-of-sample success must originate from lower-complexity artefacts rather than from the intended high-dimensional mechanism.

Large Language Models (LLMs) exhibit remarkable capabilities across a spectrum of tasks in financial services, including report generation, chatbots, sentiment analysis, regulatory compliance, investment advisory, financial knowledge retrieval, and summarization. However, their intrinsic complexity and lack of transparency pose significant challenges, especially in the highly regulated financial sector, where interpretability, fairness, and accountability are critical. As far as we are aware, this paper presents the first application in the finance domain of understanding and utilizing the inner workings of LLMs through mechanistic interpretability, addressing the pressing need for transparency and control in AI systems. Mechanistic interpretability is the most intuitive and transparent way to understand LLM behavior by reverse-engineering their internal workings. By dissecting the activations and circuits within these models, it provides insights into how specific features or components influence predictions - making it possible not only to observe but also to modify model behavior. In this paper, we explore the theoretical aspects of mechanistic interpretability and demonstrate its practical relevance through a range of financial use cases and experiments, including applications in trading strategies, sentiment analysis, bias, and hallucination detection. While not yet widely adopted, mechanistic interpretability is expected to become increasingly vital as adoption of LLMs increases. Advanced interpretability tools can ensure AI systems remain ethical, transparent, and aligned with evolving financial regulations. In this paper, we have put special emphasis on how these techniques can help unlock interpretability requirements for regulatory and compliance purposes - addressing both current needs and anticipating future expectations from financial regulators globally.

Large Language Models (LLMs) have demonstrated strong performance across various general Natural Language Processing (NLP) tasks. However, their effectiveness in financial credit assessment applications remains suboptimal, primarily due to the specialized financial expertise required for these tasks. To address this limitation, we propose ZiGong, a Mistral-based model enhanced through multi-task supervised fine-tuning. To specifically combat model hallucination in financial contexts, we introduce a novel data pruning methodology. Our approach utilizes a proxy model to score training samples, subsequently combining filtered data with original datasets for model training. This data refinement strategy effectively reduces hallucinations in LLMs while maintaining reliability in downstream financial applications. Experimental results show our method significantly enhances model robustness and prediction accuracy in real-world financial scenarios.

Financial decision-making requires processing vast amounts of real-time information while understanding their complex temporal relationships. While traditional search engines excel at providing real-time information access, they often struggle to comprehend sophisticated user intentions and contextual nuances. Conversely, Large Language Models (LLMs) demonstrate reasoning and interaction capabilities but may generate unreliable outputs without access to current data. While recent attempts have been made to combine LLMs with search capabilities, they suffer from (1) restricted access to specialized financial data, (2) static query structures that cannot adapt to dynamic market conditions, and (3) insufficient temporal awareness in result generation. To address these challenges, we present FinSearch, a novel agent-based search framework specifically designed for financial applications that interface with diverse financial data sources including market, stock, and news data. Innovatively, FinSearch comprises four components: (1) an LLM-based multi-step search pre-planner that decomposes user queries into structured sub-queries mapped to specific data sources through a graph representation; (2) a search executor with an LLM-based adaptive query rewriter that executes the searching of each sub-query while dynamically refining the sub-queries in its subsequent node based on intermediate search results; (3) a temporal weighting mechanism that prioritizes information relevance based on the deduced time context from the user's query; (4) an LLM-based response generator that synthesizes results into coherent, contextually appropriate outputs. To evaluate FinSearch, we construct FinSearchBench-24, a benchmark of 1,500 four-choice questions across the stock market, rate changes, monetary policy, and industry developments spanning from June to October 2024.

A financial market is a marketplace where financial instruments such as stocks and bonds are bought and sold (Fama 1970). Individuals and organizations can play crucial roles in financial markets to facilitate the allocation of capital. Market participants face diverse challenges, such as portfolio management, which aims to maximize investment returns over time, and market-making, which seeks to profit from the bid-ask spread while managing inventory risk. As the volume of financial data has increased dramatically over time, new opportunities and challenges have arisen in the analysis process, leading to the increased adoption of advanced Machine Learning (ML) models. Reinforcement Learning (RL)(Sutton & Barto 2018), as one of the main categories of ML, has revolutionized the field of artificial intelligence by empowering agents to interact with the environment and allowing them to learn and improve their performance. The success of RL has been demonstrated in various fields, including games, robots, mobile health (Nash Jr 1950, Kalman 1960, Murphy 2003), etc. In finance, applications such as market making, portfolio management, and order execution can benefit from the ability of RL algorithms to learn and adapt to changing environments. Compared to traditional models that rely on statistical techniques and econometric methods such as time series models (ARMA, ARIMA), factor models, and panel models, the RL framework empowers agents to learn decision-making by interacting with an environment and deducing the consequences of past actions to maximize cumulative rewards (Charpentier et al. 2021).

This paper introduces the UCFE: User-Centric Financial Expertise benchmark, an innovative framework designed to evaluate the ability of large language models (LLMs) to handle complex real-world financial tasks. UCFE benchmark adopts a hybrid approach that combines human expert evaluations with dynamic, task-specific interactions to simulate the complexities of evolving financial scenarios. Firstly, we conducted a user study involving 804 participants, collecting their feedback on financial tasks. Secondly, based on this feedback, we created our dataset that encompasses a wide range of user intents and interactions. This dataset serves as the foundation for benchmarking 12 LLM services using the LLM-as-Judge methodology. Our results show a significant alignment between benchmark scores and human preferences, with a Pearson correlation coefficient of 0.78, confirming the effectiveness of the UCFE dataset and our evaluation approach. UCFE benchmark not only reveals the potential of LLMs in the financial sector but also provides a robust framework for assessing their performance and user satisfaction. The benchmark dataset and evaluation code are available.

Synthetic Data is increasingly important in financial applications. In addition to the benefits it provides, such as improved financial modeling and better testing procedures, it poses privacy risks as well. Such data may arise from client information, business information, or other proprietary sources that must be protected. Even though the process by which Synthetic Data is generated serves to obscure the original data to some degree, the extent to which privacy is preserved is hard to assess. Accordingly, we introduce a hierarchy of ``levels'' of privacy that are useful for categorizing Synthetic Data generation methods and the progressively improved protections they offer. While the six levels were devised in the context of financial applications, they may also be appropriate for other industries as well. Our paper includes: A brief overview of Financial Synthetic Data, how it can be used, how its value can be assessed, privacy risks, and privacy attacks. We close with details of the ``Six Levels'' that include defenses against those attacks.

Recent advances in large language models (LLMs) have opened new possibilities for artificial intelligence applications in finance. In this paper, we provide a practical survey focused on two key aspects of utilizing LLMs for financial tasks: existing solutions and guidance for adoption. First, we review current approaches employing LLMs in finance, including leveraging pretrained models via zero-shot or few-shot learning, fine-tuning on domain-specific data, and training custom LLMs from scratch. We summarize key models and evaluate their performance improvements on financial natural language processing tasks. Second, we propose a decision framework to guide financial professionals in selecting the appropriate LLM solution based on their use case constraints around data, compute, and performance needs. The framework provides a pathway from lightweight experimentation to heavy investment in customized LLMs. Lastly, we discuss limitations and challenges around leveraging LLMs in financial applications. Overall, this survey aims to synthesize the state-of-the-art and provide a roadmap for responsibly applying LLMs to advance financial AI.

The basic paradigm for learning in neural networks is'learning from examples' where a training set of input-output examples is used to teach the network the target function. Learning from hints is a gen(cid:173) eralization of learning from examples where additional information about the target function can be incorporated in the same learning process. Such information can come from common sense rules or special expertise. In financial market applications where the train(cid:173) ing data is very noisy, the use of such hints can have a decisive advantage. We demonstrate the use of hints in foreign-exchange trading of the U.S. Dollar versus the British Pound, the German Mark, the Japanese Yen, and the Swiss Franc, over a period of 32 months.