Portfolio Management

Equilibrium Portfolio Selection under Utility-Variance Analysis of Log Returns in Incomplete Markets ArXiv ID: 2511.05861 “View on arXiv” Authors: Yue Cao, Zongxia Liang, Sheng Wang, Xiang Yu Abstract This paper investigates a time-inconsistent portfolio selection problem in the incomplete mar ket model, integrating expected utility maximization with risk control. The objective functional balances the expected utility and variance on log returns, giving rise to time inconsistency and motivating the search of a time-consistent equilibrium strategy. We characterize the equilibrium via a coupled quadratic backward stochastic differential equation (BSDE) system and establish the existence theory in two special cases: (i)the two Brownian motions driven the price dynamics and the factor process are independent with $ρ= 0$; (ii) the trading strategy is constrained to be bounded. For the general case with correlation coefficient $ρ\neq 0$, we introduce the notion of an approximate time-consistent equilibrium. Employing the solution structure from the equilibrium in the case $ρ= 0$, we can construct an approximate time-consistent equilibrium in the general case with an error of order $O(ρ^2)$. Numerical examples and financial insights are also presented based on deep learning algorithms. ...

Competitive optimal portfolio selection under mean-variance criterion ArXiv ID: 2511.05270 “View on arXiv” Authors: Guojiang Shao, Zuo Quan Xu, Qi Zhang Abstract We investigate a portfolio selection problem involving multi competitive agents, each exhibiting mean-variance preferences. Unlike classical models, each agent’s utility is determined by their relative wealth compared to the average wealth of all agents, introducing a competitive dynamic into the optimization framework. To address this game-theoretic problem, we first reformulate the mean-variance criterion as a constrained, non-homogeneous stochastic linear-quadratic control problem and derive the corresponding optimal feedback strategies. The existence of Nash equilibria is shown to depend on the well-posedness of a complex, coupled system of equations. Employing decoupling techniques, we reduce the well-posedness analysis to the solvability of a novel class of multi-dimensional linear backward stochastic differential equations (BSDEs). We solve a new type of nonlinear BSDEs (including the above linear one as a special case) using fixed-point theory. Depending on the interplay between market and competition parameters, three distinct scenarios arise: (i) the existence of a unique Nash equilibrium, (ii) the absence of any Nash equilibrium, and (iii) the existence of infinitely many Nash equilibria. These scenarios are rigorously characterized and discussed in detail. ...

LiveTradeBench: Seeking Real-World Alpha with Large Language Models ArXiv ID: 2511.03628 “View on arXiv” Authors: Haofei Yu, Fenghai Li, Jiaxuan You Abstract Large language models (LLMs) achieve strong performance across benchmarks–from knowledge quizzes and math reasoning to web-agent tasks–but these tests occur in static settings, lacking real dynamics and uncertainty. Consequently, they evaluate isolated reasoning or problem-solving rather than decision-making under uncertainty. To address this, we introduce LiveTradeBench, a live trading environment for evaluating LLM agents in realistic and evolving markets. LiveTradeBench follows three design principles: (i) Live data streaming of market prices and news, eliminating dependence on offline backtesting and preventing information leakage while capturing real-time uncertainty; (ii) a portfolio-management abstraction that extends control from single-asset actions to multi-asset allocation, integrating risk management and cross-asset reasoning; and (iii) multi-market evaluation across structurally distinct environments–U.S. stocks and Polymarket prediction markets–differing in volatility, liquidity, and information flow. At each step, an agent observes prices, news, and its portfolio, then outputs percentage allocations that balance risk and return. Using LiveTradeBench, we run 50-day live evaluations of 21 LLMs across families. Results show that (1) high LMArena scores do not imply superior trading outcomes; (2) models display distinct portfolio styles reflecting risk appetite and reasoning dynamics; and (3) some LLMs effectively leverage live signals to adapt decisions. These findings expose a gap between static evaluation and real-world competence, motivating benchmarks that test sequential decision making and consistency under live uncertainty. ...

Entropy-Guided Multiplicative Updates: KL Projections for Multi-Factor Target Exposures ArXiv ID: 2510.24607 “View on arXiv” Authors: Yimeng Qiu Abstract We introduce Entropy-Guided Multiplicative Updates (EGMU), a convex optimization framework for constructing multi-factor target-exposure portfolios by minimizing Kullback-Leibler divergence from a benchmark under linear factor constraints. We establish feasibility and uniqueness of strictly positive solutions when the benchmark and targets satisfy convex-hull conditions. We derive the dual concave formulation with explicit gradient, Hessian, and sensitivity expressions, and provide two provably convergent solvers: a damped dual Newton method with global convergence and local quadratic rate, and a KL-projection scheme based on iterative proportional fitting and Bregman-Dykstra projections. We further generalize EGMU to handle elastic targets and robust target sets, and introduce a path-following ordinary differential equation for tracing solution trajectories. Stable and scalable implementations are provided using LogSumExp stabilization, covariance regularization, and half-space KL projections. Our focus is on theory and reproducible algorithms; empirical benchmarking is optional. ...

FinCARE: Financial Causal Analysis with Reasoning and Evidence ArXiv ID: 2510.20221 “View on arXiv” Authors: Alejandro Michel, Abhinav Arun, Bhaskarjit Sarmah, Stefano Pasquali Abstract Portfolio managers rely on correlation-based analysis and heuristic methods that fail to capture true causal relationships driving performance. We present a hybrid framework that integrates statistical causal discovery algorithms with domain knowledge from two complementary sources: a financial knowledge graph extracted from SEC 10-K filings and large language model reasoning. Our approach systematically enhances three representative causal discovery paradigms, constraint-based (PC), score-based (GES), and continuous optimization (NOTEARS), by encoding knowledge graph constraints algorithmically and leveraging LLM conceptual reasoning for hypothesis generation. Evaluated on a synthetic financial dataset of 500 firms across 18 variables, our KG+LLM-enhanced methods demonstrate consistent improvements across all three algorithms: PC (F1: 0.622 vs. 0.459 baseline, +36%), GES (F1: 0.735 vs. 0.367, +100%), and NOTEARS (F1: 0.759 vs. 0.163, +366%). The framework enables reliable scenario analysis with mean absolute error of 0.003610 for counterfactual predictions and perfect directional accuracy for intervention effects. It also addresses critical limitations of existing methods by grounding statistical discoveries in financial domain expertise while maintaining empirical validation, providing portfolio managers with the causal foundation necessary for proactive risk management and strategic decision-making in dynamic market environments. ...

An Adaptive Multi Agent Bitcoin Trading System ArXiv ID: 2510.08068 “View on arXiv” Authors: Aadi Singhi Abstract This paper presents a Multi Agent Bitcoin Trading system that utilizes Large Language Models (LLMs) for alpha generation and portfolio management in the cryptocurrencies market. Unlike equities, cryptocurrencies exhibit extreme volatility and are heavily influenced by rapidly shifting market sentiments and regulatory announcements, making them difficult to model using static regression models or neural networks trained solely on historical data. The proposed framework overcomes this by structuring LLMs into specialised agents for technical analysis, sentiment evaluation, decision-making, and performance reflection. The agents improve over time via a novel verbal feedback mechanism where a Reflect agent provides daily and weekly natural-language critiques of trading decisions. These textual evaluations are then injected into future prompts of the agents, allowing them to adjust allocation logic without weight updates or finetuning. Back-testing on Bitcoin price data from July 2024 to April 2025 shows consistent outperformance across market regimes: the Quantitative agent delivered over 30% higher returns in bullish phases and 15% overall gains versus buy-and-hold, while the sentiment-driven agent turned sideways markets from a small loss into a gain of over 100%. Adding weekly feedback further improved total performance by 31% and reduced bearish losses by 10%. The results demonstrate that verbal feedback represents a new, scalable, and low-cost approach of tuning LLMs for financial goals. ...

Diffusion-Augmented Reinforcement Learning for Robust Portfolio Optimization under Stress Scenarios ArXiv ID: 2510.07099 “View on arXiv” Authors: Himanshu Choudhary, Arishi Orra, Manoj Thakur Abstract In the ever-changing and intricate landscape of financial markets, portfolio optimisation remains a formidable challenge for investors and asset managers. Conventional methods often struggle to capture the complex dynamics of market behaviour and align with diverse investor preferences. To address this, we propose an innovative framework, termed Diffusion-Augmented Reinforcement Learning (DARL), which synergistically integrates Denoising Diffusion Probabilistic Models (DDPMs) with Deep Reinforcement Learning (DRL) for portfolio management. By leveraging DDPMs to generate synthetic market crash scenarios conditioned on varying stress intensities, our approach significantly enhances the robustness of training data. Empirical evaluations demonstrate that DARL outperforms traditional baselines, delivering superior risk-adjusted returns and resilience against unforeseen crises, such as the 2025 Tariff Crisis. This work offers a robust and practical methodology to bolster stress resilience in DRL-driven financial applications. ...

A Practitioner’s Guide to AI+ML in Portfolio Investing ArXiv ID: 2509.25456 “View on arXiv” Authors: Mehmet Caner Qingliang Fan Abstract In this review, we provide practical guidance on some of the main machine learning tools used in portfolio weight formation. This is not an exhaustive list, but a fraction of the ones used and have some statistical analysis behind it. All this research is essentially tied to precision matrix of excess asset returns. Our main point is that the techniques should be used in conjunction with outlined objective functions. In other words, there should be joint analysis of Machine Learning (ML) technique with the possible portfolio choice-objective functions in terms of test period Sharpe Ratio or returns. The ML method with the best objective function should provide the weight for portfolio formation. Empirically we analyze five time periods of interest, that are out-sample and show performance of some ML-Artificial Intelligence (AI) methods. We see that nodewise regression with Global Minimum Variance portfolio based weights deliver very good Sharpe Ratio and returns across five time periods in this century we analyze. We cover three downturns, and 2 long term investment spans. ...

Optimal Consumption-Investment with Epstein-Zin Utility under Leverage Constraint ArXiv ID: 2509.21929 “View on arXiv” Authors: Dejian Tian, Weidong Tian, Jianjun Zhou, Zimu Zhu Abstract We study optimal portfolio choice under Epstein-Zin recursive utility in the presence of general leverage constraints. We first establish that the optimal value function is the unique viscosity solution to the associated Hamilton-Jacobi-Bellman (HJB) equation, by developing a new dynamic programming principle under constraints. We further demonstrate that the value function admits smoothness and characterize the optimal consumption and investment strategies. In addition, we derive explicit solutions for the optimal strategy and explicitly delineate the constrained and unconstrained regions in several special cases of the leverage constraint. Finally, we conduct a comparative analysis, highlighting the differences relative to the classical time-separable preferences and to the setting without leverage constraints. ...

Portfolio Analysis Based on Markowitz Stochastic Dominance Criteria: A Behavioral Perspective ArXiv ID: 2509.22896 “View on arXiv” Authors: Peng Xu Abstract This paper develops stochastic optimization problems for describing and analyzing behavioral investors with Markowitz Stochastic Dominance (MSD) preferences. Specifically, we establish dominance conditions in a discrete state-space to capture all reverse S-shaped MSD preferences as well as all subjective decision weights generated by inverse S-shaped probability weighting functions. We demonstrate that these dominance conditions can be admitted as linear constraints into the stochastic optimization problems to formulate computationally tractable mixed-integer linear programming (MILP) models. We then employ the developed MILP models in financial portfolio analysis and examine classic behavioral factors such as reference point and subjective probability distortion in behavioral investors’ portfolio decisions. ...