Law-Strength Frontiers and a No-Free-Lunch Result for Law-Seeking Reinforcement Learning on Volatility Law Manifolds ArXiv ID: 2511.17304 “View on arXiv” Authors: Jian’an Zhang Abstract We study reinforcement learning (RL) on volatility surfaces through the lens of Scientific AI. We ask whether axiomatic no-arbitrage laws, imposed as soft penalties on a learned world model, can reliably align high-capacity RL agents, or mainly create Goodhart-style incentives to exploit model errors. From classical static no-arbitrage conditions we build a finite-dimensional convex volatility law manifold of admissible total-variance surfaces, together with a metric law-penalty functional and a Graceful Failure Index (GFI) that normalizes law degradation under shocks. A synthetic generator produces law-consistent trajectories, while a recurrent neural world model trained without law regularization exhibits structured off-manifold errors. On this testbed we define a Goodhart decomposition (r = r^{"\mathcal{M"}} + r^\perp), where (r^\perp) is ghost arbitrage from off-manifold prediction error. We prove a ghost-arbitrage incentive theorem for PPO-type agents, a law-strength trade-off theorem showing that stronger penalties eventually worsen P&L, and a no-free-lunch theorem: under a law-consistent world model and law-aligned strategy class, unconstrained law-seeking RL cannot Pareto-dominate structural baselines on P&L, penalties, and GFI. In experiments on an SPX/VIX-like world model, simple structural strategies form the empirical law-strength frontier, while all law-seeking RL variants underperform and move into high-penalty, high-GFI regions. Volatility thus provides a concrete case where reward shaping with verifiable penalties is insufficient for robust law alignment. ...

Scaling Conditional Autoencoders for Portfolio Optimization via Uncertainty-Aware Factor Selection ArXiv ID: 2511.17462 “View on arXiv” Authors: Ryan Engel, Yu Chen, Pawel Polak, Ioana Boier Abstract Conditional Autoencoders (CAEs) offer a flexible, interpretable approach for estimating latent asset-pricing factors from firm characteristics. However, existing studies usually limit the latent factor dimension to around K=5 due to concerns that larger K can degrade performance. To overcome this challenge, we propose a scalable framework that couples a high-dimensional CAE with an uncertainty-aware factor selection procedure. We employ three models for quantile prediction: zero-shot Chronos, a pretrained time-series foundation model (ZS-Chronos), gradient-boosted quantile regression trees using XGBoost and RAPIDS (Q-Boost), and an I.I.D bootstrap-based sample mean model (IID-BS). For each model, we rank factors by forecast uncertainty and retain the top-k most predictable factors for portfolio construction, where k denotes the selected subset of factors. This pruning strategy delivers substantial gains in risk-adjusted performance across all forecasting models. Furthermore, due to each model’s uncorrelated predictions, a performance-weighted ensemble consistently outperforms individual models with higher Sharpe, Sortino, and Omega ratios. ...

Financial Information Theory ArXiv ID: 2511.16339 “View on arXiv” Authors: Miquel Noguer i Alonso Abstract This paper introduces a comprehensive framework for Financial Information Theory by applying information-theoretic concepts such as entropy, Kullback-Leibler divergence, mutual information, normalized mutual information, and transfer entropy to financial time series. We systematically derive these measures with complete mathematical proofs, establish their theoretical properties, and propose practical algorithms for estimation. Using S&P 500 data from 2000 to 2025, we demonstrate empirical usefulness for regime detection, market efficiency testing, and portfolio construction. We show that normalized mutual information (NMI) behaves as a powerful, bounded, and interpretable measure of temporal dependence, highlighting periods of structural change such as the 2008 financial crisis and the COVID-19 shock. Our entropy-adjusted Value at Risk, information-theoretic diversification criterion, and NMI-based market efficiency test provide actionable tools for risk management and asset allocation. We interpret NMI as a quantitative diagnostic of the Efficient Market Hypothesis and demonstrate that information-theoretic methods offer superior regime detection compared to traditional autocorrelation- or volatility-based approaches. All theoretical results include rigorous proofs, and empirical findings are validated across multiple market regimes spanning 25 years of daily returns. ...

Integration of LSTM Networks in Random Forest Algorithms for Stock Market Trading Predictions ArXiv ID: 2512.02036 “View on arXiv” Authors: Juan C. King, Jose M. Amigo Abstract The aim of this paper is the analysis and selection of stock trading systems that combine different models with data of different nature, such as financial and microeconomic information. Specifically, based on previous work by the authors and applying advanced techniques of Machine Learning and Deep Learning, our objective is to formulate trading algorithms for the stock market with empirically tested statistical advantages, thus improving results published in the literature. Our approach integrates Long Short-Term Memory (LSTM) networks with algorithms based on decision trees, such as Random Forest and Gradient Boosting. While the former analyze price patterns of financial assets, the latter are fed with economic data of companies. Numerical simulations of algorithmic trading with data from international companies and 10-weekday predictions confirm that an approach based on both fundamental and technical variables can outperform the usual approaches, which do not combine those two types of variables. In doing so, Random Forest turned out to be the best performer among the decision trees. We also discuss how the prediction performance of such a hybrid approach can be boosted by selecting the technical variables. ...

Machine Learning vs. Randomness: Challenges in Predicting Binary Options Movements ArXiv ID: 2511.15960 “View on arXiv” Authors: Gabriel M. Arantes, Richard F. Pinto, Bruno L. Dalmazo, Eduardo N. Borges, Giancarlo Lucca, Viviane L. D. de Mattos, Fabian C. Cardoso, Rafael A. Berri Abstract Binary options trading is often marketed as a field where predictive models can generate consistent profits. However, the inherent randomness and stochastic nature of binary options make price movements highly unpredictable, posing significant challenges for any forecasting approach. This study demonstrates that machine learning algorithms struggle to outperform a simple baseline in predicting binary options movements. Using a dataset of EUR/USD currency pairs from 2021 to 2023, we tested multiple models, including Random Forest, Logistic Regression, Gradient Boosting, and k-Nearest Neighbors (kNN), both before and after hyperparameter optimization. Furthermore, several neural network architectures, including Multi-Layer Perceptrons (MLP) and a Long Short-Term Memory (LSTM) network, were evaluated under different training conditions. Despite these exhaustive efforts, none of the models surpassed the ZeroR baseline accuracy, highlighting the inherent randomness of binary options. These findings reinforce the notion that binary options lack predictable patterns, making them unsuitable for machine learning-based forecasting. ...

Statistical Arbitrage in Polish Equities Market Using Deep Learning Techniques ArXiv ID: 2512.02037 “View on arXiv” Authors: Marek Adamczyk, Michał Dąbrowski Abstract We study a systematic approach to a popular Statistical Arbitrage technique: Pairs Trading. Instead of relying on two highly correlated assets, we replace the second asset with a replication of the first using risk factor representations. These factors are obtained through Principal Components Analysis (PCA), exchange traded funds (ETFs), and, as our main contribution, Long Short Term Memory networks (LSTMs). Residuals between the main asset and its replication are examined for mean reversion properties, and trading signals are generated for sufficiently fast mean reverting portfolios. Beyond introducing a deep learning based replication method, we adapt the framework of Avellaneda and Lee (2008) to the Polish market. Accordingly, components of WIG20, mWIG40, and selected sector indices replace the original S&P500 universe, and market parameters such as the risk free rate and transaction costs are updated to reflect local conditions. We outline the full strategy pipeline: risk factor construction, residual modeling via the Ornstein Uhlenbeck process, and signal generation. Each replication technique is described together with its practical implementation. Strategy performance is evaluated over two periods: 2017-2019 and the recessive year 2020. All methods yield profits in 2017-2019, with PCA achieving roughly 20 percent cumulative return and an annualized Sharpe ratio of up to 2.63. Despite multiple adaptations, our conclusions remain consistent with those of the original paper. During the COVID-19 recession, only the ETF based approach remains profitable (about 5 percent annual return), while PCA and LSTM methods underperform. LSTM results, although negative, are promising and indicate potential for future optimization. ...

HODL Strategy or Fantasy? 480 Million Crypto Market Simulations and the Macro-Sentiment Effect ArXiv ID: 2512.02029 “View on arXiv” Authors: Weikang Zhang, Alison Watts Abstract Crypto enthusiasts claim that buying and holding crypto assets yields high returns, often citing Bitcoin’s past performance to promote other tokens and fuel fear of missing out. However, understanding the real risk-return trade-off and what factors affect future crypto returns is crucial as crypto becomes increasingly accessible to retail investors through major brokerages. We examine the HODL strategy through two independent analyses. First, we implement 480 million Monte Carlo simulations across 378 non-stablecoin crypto assets, net of trading fees and the opportunity cost of 1-month Treasury bills, and find strong evidence of survivorship bias and extreme downside concentration. At the 2-3 year horizon, the median excess return is -28.4 percent, the 1 percent conditional value at risk indicates that tail scenarios wipe out principal after all costs, and only the top quartile achieves very large gains, with a mean excess return of 1,326.7 percent. These results challenge the HODL narrative: across a broad set of assets, simple buy-and-hold loads extreme downside risk onto most investors, and the miracles mostly belong to the luckiest quarter. Second, using a Bayesian multi-horizon local projection framework, we find that endogenous predictors based on realized risk-return metrics have economically negligible and unstable effects, while macro-finance factors, especially the 24-week exponential moving average of the Fear and Greed Index, display persistent long-horizon impacts and high cross-basket stability. Where significant, a one-standard-deviation sentiment shock reduces forward top-quartile mean excess returns by 15-22 percentage points and median returns by 6-10 percentage points over 1-3 year horizons, suggesting that macro-sentiment conditions, rather than realized return histories, are the dominant indicators for future outcomes. ...

Reinforcement Learning in Queue-Reactive Models: Application to Optimal Execution ArXiv ID: 2511.15262 “View on arXiv” Authors: Tomas Espana, Yadh Hafsi, Fabrizio Lillo, Edoardo Vittori Abstract We investigate the use of Reinforcement Learning for the optimal execution of meta-orders, where the objective is to execute incrementally large orders while minimizing implementation shortfall and market impact over an extended period of time. Departing from traditional parametric approaches to price dynamics and impact modeling, we adopt a model-free, data-driven framework. Since policy optimization requires counterfactual feedback that historical data cannot provide, we employ the Queue-Reactive Model to generate realistic and tractable limit order book simulations that encompass transient price impact, and nonlinear and dynamic order flow responses. Methodologically, we train a Double Deep Q-Network agent on a state space comprising time, inventory, price, and depth variables, and evaluate its performance against established benchmarks. Numerical simulation results show that the agent learns a policy that is both strategic and tactical, adapting effectively to order book conditions and outperforming standard approaches across multiple training configurations. These findings provide strong evidence that model-free Reinforcement Learning can yield adaptive and robust solutions to the optimal execution problem. ...

The Hidden Constant of Market Rhythms: How $1-1/e$ Defines Scaling in Intrinsic Time ArXiv ID: 2511.14408 “View on arXiv” Authors: Thomas Houweling Abstract Directional-change Intrinsic Time analysis has long revealed scaling laws in market microstructure, but the origin of their stability remains elusive. This article presents evidence that Intrinsic Time can be modeled as a memoryless exponential hazard process. Empirically, the proportion of directional changes to total events stabilizes near $1 - 1/e = 0.632$, matching the probability that a Poisson process completes one mean interval. This constant provides a natural heuristic to identify scaling regimes across thresholds and supports an interpretation of market activity as a renewal process in intrinsic time. ...

Basis Immunity: Isotropy as a Regularizer for Uncertainty ArXiv ID: 2511.13334 “View on arXiv” Authors: Florent Segonne Abstract Diversification is a cornerstone of robust portfolio construction, yet its application remains fraught with challenges due to model uncertainty and estimation errors. Practitioners often rely on sophisticated, proprietary heuristics to navigate these issues. Among recent advancements, Agnostic Risk Parity introduces eigenrisk parity (ERP), an innovative approach that leverages isotropy to evenly allocate risk across eigenmodes, enhancing portfolio stability. In this paper, we review and extend the isotropy-enforced philosophy of ERP proposing a versatile framework that integrates mean-variance optimization with an isotropy constraint acting as a geometric regularizer against signal uncertainty. The resulting allocations decompose naturally into canonical portfolios, smoothly interpolating between full isotropy (closed-form isotropic-mean allocation) and pure mean-variance through a tunable isotropy penalty. Beyond methodology, we revisit fundamental concepts and clarify foundational links between isotropy, canonical portfolios, principal portfolios, primal versus dual representations, and intrinsic basis-invariant metrics for returns, risk, and isotropy. Applied to sector trend-following, the isotropy constraint systematically induces negative average-signal exposure – a structural, parameter-robust crash hedge. This work offers both a practical, theoretically grounded tool for resilient allocation under signal uncertainty and a pedagogical synthesis of modern portfolio concepts. ...