Multi-Asset

Bayesian Portfolio Optimization by Predictive Synthesis ArXiv ID: 2510.07180 “View on arXiv” Authors: Masahiro Kato, Kentaro Baba, Hibiki Kaibuchi, Ryo Inokuchi Abstract Portfolio optimization is a critical task in investment. Most existing portfolio optimization methods require information on the distribution of returns of the assets that make up the portfolio. However, such distribution information is usually unknown to investors. Various methods have been proposed to estimate distribution information, but their accuracy greatly depends on the uncertainty of the financial markets. Due to this uncertainty, a model that could well predict the distribution information at one point in time may perform less accurately compared to another model at a different time. To solve this problem, we investigate a method for portfolio optimization based on Bayesian predictive synthesis (BPS), one of the Bayesian ensemble methods for meta-learning. We assume that investors have access to multiple asset return prediction models. By using BPS with dynamic linear models to combine these predictions, we can obtain a Bayesian predictive posterior about the mean rewards of assets that accommodate the uncertainty of the financial markets. In this study, we examine how to construct mean-variance portfolios and quantile-based portfolios based on the predicted distribution information. ...

From Classical Rationality to Contextual Reasoning: Quantum Logic as a New Frontier for Human-Centric AI in Finance ArXiv ID: 2510.05475 “View on arXiv” Authors: Fabio Bagarello, Francesco Gargano, Polina Khrennikova Abstract We consider state of the art applications of artificial intelligence (AI) in modelling human financial expectations and explore the potential of quantum logic to drive future advancements in this field. This analysis highlights the application of machine learning techniques, including reinforcement learning and deep neural networks, in financial statement analysis, algorithmic trading, portfolio management, and robo-advisory services. We further discuss the emergence and progress of quantum machine learning (QML) and advocate for broader exploration of the advantages provided by quantum-inspired neural networks. ...

Non-conservative optimal transport ArXiv ID: 2510.03332 “View on arXiv” Authors: Gabriela Kováčová, Georg Menz, Niket Patel Abstract Motivated by optimal re-balancing of a portfolio, we formalize an optimal transport problem in which the transported mass is scaled by a mass-change factor depending on the source and destination. This allows direct modeling of the creation or destruction of mass. We discuss applications and position the framework alongside unbalanced, entropic, and unnormalized optimal transport. The existence of optimal transport plans and strong duality are established. The existence of optimal maps are deduced in two central regimes, i.e., perturbative mass-change and quadratic mass-loss. For $\ell_p$ costs we derive the analogue of the Benamou-Brenier dynamic formulation. ...

Adaptive and Regime-Aware RL for Portfolio Optimization ArXiv ID: 2509.14385 “View on arXiv” Authors: Gabriel Nixon Raj Abstract This study proposes a regime-aware reinforcement learning framework for long-horizon portfolio optimization. Moving beyond traditional feedforward and GARCH-based models, we design realistic environments where agents dynamically reallocate capital in response to latent macroeconomic regime shifts. Agents receive hybrid observations and are trained using constrained reward functions that incorporate volatility penalties, capital resets, and tail-risk shocks. We benchmark multiple architectures, including PPO, LSTM-based PPO, and Transformer PPO, against classical baselines such as equal-weight and Sharpe-optimized portfolios. Our agents demonstrate robust performance under financial stress. While Transformer PPO achieves the highest risk-adjusted returns, LSTM variants offer a favorable trade-off between interpretability and training cost. The framework promotes regime-adaptive, explainable reinforcement learning for dynamic asset allocation. ...

Robust MCVaR Portfolio Optimization with Ellipsoidal Support and Reproducing Kernel Hilbert Space-based Uncertainty ArXiv ID: 2509.00447 “View on arXiv” Authors: Rupendra Yadav, Aparna Mehra Abstract This study introduces a portfolio optimization framework to minimize mixed conditional value at risk (MCVaR), incorporating a chance constraint on expected returns and limiting the number of assets via cardinality constraints. A robust MCVaR model is presented, which presumes ellipsoidal support for random returns without assuming any distribution. The model utilizes an uncertainty set grounded in a reproducing kernel Hilbert space (RKHS) to manage the chance constraint, resulting in a simplified second-order cone programming (SOCP) formulation. The performance of the robust model is tested on datasets from six distinct financial markets. The outcomes of comprehensive experiments indicate that the robust model surpasses the nominal model, market portfolio, and equal-weight portfolio with higher expected returns, lower risk metrics, enhanced reward-risk ratios, and a better value of Jensen’s alpha in many cases. Furthermore, we aim to validate the robust models in different market phases (bullish, bearish, and neutral). The robust model shows a distinct advantage in bear markets, providing better risk protection against adverse conditions. In contrast, its performance in bullish and neutral phases is somewhat similar to that of the nominal model. The robust model appears effective in volatile markets, although further research is necessary to comprehend its performance across different market conditions. ...

An Interval Type-2 Version of Bayes Theorem Derived from Interval Probability Range Estimates Provided by Subject Matter Experts ArXiv ID: 2509.08834 “View on arXiv” Authors: John T. Rickard, William A. Dembski, James Rickards Abstract Bayesian inference is widely used in many different fields to test hypotheses against observations. In most such applications, an assumption is made of precise input values to produce a precise output value. However, this is unrealistic for real-world applications. Often the best available information from subject matter experts (SMEs) in a given field is interval range estimates of the input probabilities involved in Bayes Theorem. This paper provides two key contributions to extend Bayes Theorem to an interval type-2 (IT2) version. First, we develop an IT2 version of Bayes Theorem that uses a novel and conservative method to avoid potential inconsistencies in the input IT2 MFs that otherwise might produce invalid output results. We then describe a novel and flexible algorithm for encoding SME-provided intervals into IT2 fuzzy membership functions (MFs), which we can use to specify the input probabilities in Bayes Theorem. Our algorithm generalizes and extends previous work on this problem that primarily addressed the encoding of intervals into word MFs for Computing with Words applications. ...

Deep Reinforcement Learning for Optimal Asset Allocation Using DDPG with TiDE ArXiv ID: 2508.20103 “View on arXiv” Authors: Rongwei Liu, Jin Zheng, John Cartlidge Abstract The optimal asset allocation between risky and risk-free assets is a persistent challenge due to the inherent volatility in financial markets. Conventional methods rely on strict distributional assumptions or non-additive reward ratios, which limit their robustness and applicability to investment goals. To overcome these constraints, this study formulates the optimal two-asset allocation problem as a sequential decision-making task within a Markov Decision Process (MDP). This framework enables the application of reinforcement learning (RL) mechanisms to develop dynamic policies based on simulated financial scenarios, regardless of prerequisites. We use the Kelly criterion to balance immediate reward signals against long-term investment objectives, and we take the novel step of integrating the Time-series Dense Encoder (TiDE) into the Deep Deterministic Policy Gradient (DDPG) RL framework for continuous decision-making. We compare DDPG-TiDE with a simple discrete-action Q-learning RL framework and a passive buy-and-hold investment strategy. Empirical results show that DDPG-TiDE outperforms Q-learning and generates higher risk adjusted returns than buy-and-hold. These findings suggest that tackling the optimal asset allocation problem by integrating TiDE within a DDPG reinforcement learning framework is a fruitful avenue for further exploration. ...

Can LLMs Identify Tax Abuse? ArXiv ID: 2508.20097 “View on arXiv” Authors: Andrew Blair-Stanek, Nils Holzenberger, Benjamin Van Durme Abstract We investigate whether large language models can discover and analyze U.S. tax-minimization strategies. This real-world domain challenges even seasoned human experts, and progress can reduce tax revenue lost from well-advised, wealthy taxpayers. We evaluate the most advanced LLMs on their ability to (1) interpret and verify tax strategies, (2) fill in gaps in partially specified strategies, and (3) generate complete, end-to-end strategies from scratch. This domain should be of particular interest to the LLM reasoning community: unlike synthetic challenge problems or scientific reasoning tasks, U.S. tax law involves navigating hundreds of thousands of pages of statutes, case law, and administrative guidance, all updated regularly. Notably, LLM-based reasoning identified an entirely novel tax strategy, highlighting these models’ potential to revolutionize tax agencies’ fight against tax abuse. ...

Temperature Measurement in Agent Systems ArXiv ID: 2507.08394 “View on arXiv” Authors: Christoph J. Börner, Ingo Hoffmann Abstract Models for spin systems, known from statistical physics, are applied analogously in econometrics in the form of agent-based models. The models discussed in the econophysics literature all use the state variable $T$, which, in physics, represents the temperature of a system. However, there is little evidence on how temperature can be measured in econophysics, so that the models can be applied. Only in idealized capital market applications has the relationship between temperature and volatility been demonstrated, allowing temperature to be determined through volatility measurements. The question remains how this can be achieved in agent systems beyond capital market applications. This paper focuses precisely on this question. It examines an agent system with two decision options in a news environment, establishes the measurement equation, and outlines the basic concept of temperature measurement. The procedure is illustrated using an example. In an application with competing subsystems, an interesting strategy for influencing the average opinion in the competing subsystem is presented. ...

Advancing Financial Engineering with Foundation Models: Progress, Applications, and Challenges ArXiv ID: 2507.18577 “View on arXiv” Authors: Liyuan Chen, Shuoling Liu, Jiangpeng Yan, Xiaoyu Wang, Henglin Liu, Chuang Li, Kecheng Jiao, Jixuan Ying, Yang Veronica Liu, Qiang Yang, Xiu Li Abstract The advent of foundation models (FMs), large-scale pre-trained models with strong generalization capabilities, has opened new frontiers for financial engineering. While general-purpose FMs such as GPT-4 and Gemini have demonstrated promising performance in tasks ranging from financial report summarization to sentiment-aware forecasting, many financial applications remain constrained by unique domain requirements such as multimodal reasoning, regulatory compliance, and data privacy. These challenges have spurred the emergence of financial foundation models (FFMs): a new class of models explicitly designed for finance. This survey presents a comprehensive overview of FFMs, with a taxonomy spanning three key modalities: financial language foundation models (FinLFMs), financial time-series foundation models (FinTSFMs), and financial visual-language foundation models (FinVLFMs). We review their architectures, training methodologies, datasets, and real-world applications. Furthermore, we identify critical challenges in data availability, algorithmic scalability, and infrastructure constraints and offer insights into future research opportunities. We hope this survey can serve as both a comprehensive reference for understanding FFMs and a practical roadmap for future innovation. ...