A Global Optimal Theory of Portfolio beyond R-$σ$ Model ArXiv ID: 2601.00281 “View on arXiv” Authors: Yifan Liu, Shi-Dong Liang Abstract The deviation of the efficient market hypothesis (EMH) for the practical economic system allows us gain the arbitrary or risk premium in finance markets. We propose the triplet $(R,H,σ)$ theory to give the local and global optimal portfolio, which eneralize from the $(R,σ)$ model. We present the formulation of the triplet $(R,H,σ)$ model and give the Pareto optimal solution as well as comparing it with the numerical investigations for the Chinese stock market. We define the local optimal weights of the triplet $(\mathbf{“w”}{“R”},\mathbf{“w”}{“H”},\mathbf{“w”}_σ)$, which constructs the triangle of the quasi-optimal investing subspace such that we further define the centroid of the triangle or the incenter of the triangle as the optimal investing weights, which optimizes the mean return, the arbitrary or risk premium and the volatility risk. By investigating numerically the Chinese stock market as an example we demonstrate the validity of the formulation and obtain the global optimal strategy and quasi-optimal investing subspace. The theory provides an efficient way to design the portfolio for different style investors, conservative or aggressive investors, in finance market to maximize the mean return and arbitrary or risk premium with a small volatility risk. ...

Core-Periphery Dynamics in Market-Conditioned Financial Networks: A Conditional P-Threshold Mutual Information Approach ArXiv ID: 2601.00395 “View on arXiv” Authors: Kundan Mukhia, Imran Ansari, S R Luwang, Md Nurujjaman Abstract This study investigates how financial market structure reorganizes during the COVID-19 crash using a conditional p-threshold mutual information (MI) based Minimum Spanning Tree (MST) framework. We analyze nonlinear dependencies among the largest stocks from four diverse QUAD countries: the US, Japan, Australia, and India. Crashes are identified using the Hellinger distance and Hilbert spectrum; a crash occurs when HD = mu_H + 2*sigma_H, segmenting data into pre-crash, crash, and post-crash periods. Conditional p-threshold MI filters out common market effects and applies permutation-based significance testing. Resulting validated dependencies are used to construct MST networks for comparison across periods. Networks become more integrated during the crash, with shorter path lengths, higher centrality, and lower algebraic connectivity, indicating fragility. Core-periphery structure declines, with increased periphery vulnerability, and disassortative mixing facilitates shock transmission. Post-crash networks show only partial recovery. Aftershock analysis using the Gutenberg-Richter law indicates higher relative frequency of large volatility events following the crash. Results are consistent across all markets, highlighting the conditional p-threshold MI framework for capturing nonlinear interdependencies and systemic vulnerability. ...

Multimodal Insights into Credit Risk Modelling: Integrating Climate and Text Data for Default Prediction ArXiv ID: 2601.00478 “View on arXiv” Authors: Zongxiao Wu, Ran Liu, Jiang Dai, Dan Luo Abstract Credit risk assessment increasingly relies on diverse sources of information beyond traditional structured financial data, particularly for micro and small enterprises (mSEs) with limited financial histories. This study proposes a multimodal framework that integrates structured credit variables, climate panel data, and unstructured textual narratives within a unified learning architecture. Specifically, we use long short-term memory (LSTM), the gated recurrent unit (GRU), and transformer models to analyse the interplay between these data modalities. The empirical results demonstrate that unimodal models based on climate or text data outperform those relying solely on structured data, while the integration of multiple data modalities yields significant improvements in credit default prediction. Using SHAP-based explainability methods, we find that physical climate risks play an important role in default prediction, with water-logging by rain emerging as the most influential factor. Overall, this study demonstrates the potential of multimodal approaches in AI-enabled decision-making, which provides robust tools for credit risk assessment while contributing to the broader integration of environmental and textual insights into predictive analytics. ...

Boundary error control for numerical solution of BSDEs by the convolution-FFT method ArXiv ID: 2512.24714 “View on arXiv” Authors: Xiang Gao, Cody Hyndman Abstract We first review the convolution fast-Fourier-transform (CFFT) approach for the numerical solution of backward stochastic differential equations (BSDEs) introduced in (Hyndman and Oyono Ngou, 2017). We then propose a method for improving the boundary errors obtained when valuing options using this approach. We modify the damping and shifting schemes used in the original formulation, which transforms the target function into a bounded periodic function so that Fourier transforms can be applied successfully. Time-dependent shifting reduces boundary error significantly. We present numerical results for our implementation and provide a detailed error analysis showing the improved accuracy and convergence of the modified convolution method. ...

Convergence of the generalization error for deep gradient flow methods for PDEs ArXiv ID: 2512.25017 “View on arXiv” Authors: Chenguang Liu, Antonis Papapantoleon, Jasper Rou Abstract The aim of this article is to provide a firm mathematical foundation for the application of deep gradient flow methods (DGFMs) for the solution of (high-dimensional) partial differential equations (PDEs). We decompose the generalization error of DGFMs into an approximation and a training error. We first show that the solution of PDEs that satisfy reasonable and verifiable assumptions can be approximated by neural networks, thus the approximation error tends to zero as the number of neurons tends to infinity. Then, we derive the gradient flow that the training process follows in the ``wide network limit’’ and analyze the limit of this flow as the training time tends to infinity. These results combined show that the generalization error of DGFMs tends to zero as the number of neurons and the training time tend to infinity. ...

Forward-Oriented Causal Observables for Non-Stationary Financial Markets ArXiv ID: 2512.24621 “View on arXiv” Authors: Lucas A. Souza Abstract We study short-horizon forecasting in financial time series under strict causal constraints, treating the market as a non-stationary stochastic system in which any predictive observable must be computable online from information available up to the decision time. Rather than proposing a machine-learning predictor or a direct price-forecast model, we focus on \emph{“constructing”} an interpretable causal signal from heterogeneous micro-features that encode complementary aspects of the dynamics (momentum, volume pressure, trend acceleration, and volatility-normalized price location). The construction combines (i) causal centering, (ii) linear aggregation into a composite observable, (iii) causal stabilization via a one-dimensional Kalman filter, and (iv) an adaptive ``forward-like’’ operator that mixes the composite signal with a smoothed causal derivative term. The resulting observable is mapped into a transparent decision functional and evaluated through realized cumulative returns and turnover. An application to high-frequency EURUSDT (1-minute) illustrates that causally constructed observables can exhibit substantial economic relevance in specific regimes, while degrading under subsequent regime shifts, highlighting both the potential and the limitations of causal signal design in non-stationary markets. ...

Generative AI-enhanced Sector-based Investment Portfolio Construction ArXiv ID: 2512.24526 “View on arXiv” Authors: Alina Voronina, Oleksandr Romanko, Ruiwen Cao, Roy H. Kwon, Rafael Mendoza-Arriaga Abstract This paper investigates how Large Language Models (LLMs) from leading providers (OpenAI, Google, Anthropic, DeepSeek, and xAI) can be applied to quantitative sector-based portfolio construction. We use LLMs to identify investable universes of stocks within S&P 500 sector indices and evaluate how their selections perform when combined with classical portfolio optimization methods. Each model was prompted to select and weight 20 stocks per sector, and the resulting portfolios were compared with their respective sector indices across two distinct out-of-sample periods: a stable market phase (January-March 2025) and a volatile phase (April-June 2025). Our results reveal a strong temporal dependence in LLM portfolio performance. During stable market conditions, LLM-weighted portfolios frequently outperformed sector indices on both cumulative return and risk-adjusted (Sharpe ratio) measures. However, during the volatile period, many LLM portfolios underperformed, suggesting that current models may struggle to adapt to regime shifts or high-volatility environments underrepresented in their training data. Importantly, when LLM-based stock selection is combined with traditional optimization techniques, portfolio outcomes improve in both performance and consistency. This study contributes one of the first multi-model, cross-provider evaluations of generative AI algorithms in investment management. It highlights that while LLMs can effectively complement quantitative finance by enhancing stock selection and interpretability, their reliability remains market-dependent. The findings underscore the potential of hybrid AI-quantitative frameworks, integrating LLM reasoning with established optimization techniques, to produce more robust and adaptive investment strategies. ...

Utility Maximisation with Model-independent Constraints ArXiv ID: 2512.24371 “View on arXiv” Authors: Alexander M. G. Cox, Daniel Hernandez-Hernandez Abstract We consider an agent who has access to a financial market, including derivative contracts, who looks to maximise her utility. Whilst the agent looks to maximise utility over one probability measure, or class of probability measures, she must also ensure that the mark-to-market value of her portfolio remains above a given threshold. When the mark-to-market value is based on a more pessimistic valuation method, such as model-independent bounds, we recover a novel optimisation problem for the agent where the agents investment problem must satisfy a pathwise constraint. For complete markets, the expression of the optimal terminal wealth is given, using the max-plus decomposition for supermartingales. Moreover, for the Black-Scholes-Merton model the explicit form of the process involved in such decomposition is obtained, and we are able to investigate numerically optimal portfolios in the presence of options which are mispriced according to the agent’s beliefs. ...

A Test of Lookahead Bias in LLM Forecasts ArXiv ID: 2512.23847 “View on arXiv” Authors: Zhenyu Gao, Wenxi Jiang, Yutong Yan Abstract We develop a statistical test to detect lookahead bias in economic forecasts generated by large language models (LLMs). Using state-of-the-art pre-training data detection techniques, we estimate the likelihood that a given prompt appeared in an LLM’s training corpus, a statistic we term Lookahead Propensity (LAP). We formally show that a positive correlation between LAP and forecast accuracy indicates the presence and magnitude of lookahead bias, and apply the test to two forecasting tasks: news headlines predicting stock returns and earnings call transcripts predicting capital expenditures. Our test provides a cost-efficient, diagnostic tool for assessing the validity and reliability of LLM-generated forecasts. ...

Alpha-R1: Alpha Screening with LLM Reasoning via Reinforcement Learning ArXiv ID: 2512.23515 “View on arXiv” Authors: Zuoyou Jiang, Li Zhao, Rui Sun, Ruohan Sun, Zhongjian Li, Jing Li, Daxin Jiang, Zuo Bai, Cheng Hua Abstract Signal decay and regime shifts pose recurring challenges for data-driven investment strategies in non-stationary markets. Conventional time-series and machine learning approaches, which rely primarily on historical correlations, often struggle to generalize when the economic environment changes. While large language models (LLMs) offer strong capabilities for processing unstructured information, their potential to support quantitative factor screening through explicit economic reasoning remains underexplored. Existing factor-based methods typically reduce alphas to numerical time series, overlooking the semantic rationale that determines when a factor is economically relevant. We propose Alpha-R1, an 8B-parameter reasoning model trained via reinforcement learning for context-aware alpha screening. Alpha-R1 reasons over factor logic and real-time news to evaluate alpha relevance under changing market conditions, selectively activating or deactivating factors based on contextual consistency. Empirical results across multiple asset pools show that Alpha-R1 consistently outperforms benchmark strategies and exhibits improved robustness to alpha decay. The full implementation and resources are available at https://github.com/FinStep-AI/Alpha-R1. ...