Portfolio Optimization

Covariance-Aware Simplex Projection for Cardinality-Constrained Portfolio Optimization ArXiv ID: 2512.19986 “View on arXiv” Authors: Nikolaos Iliopoulos Abstract Metaheuristic algorithms for cardinality-constrained portfolio optimization require repair operators to map infeasible candidates onto the feasible region. Standard Euclidean projection treats assets as independent and can ignore the covariance structure that governs portfolio risk, potentially producing less diversified portfolios. This paper introduces Covariance-Aware Simplex Projection (CASP), a two-stage repair operator that (i) selects a target number of assets using volatility-normalized scores and (ii) projects the candidate weights using a covariance-aware geometry aligned with tracking-error risk. This provides a portfolio-theoretic foundation for using a covariance-induced distance in repair operators. On S&P 500 data (2020-2024), CASP-Basic delivers materially lower portfolio variance than standard Euclidean repair without relying on return estimates, with improvements that are robust across assets and statistically significant. Ablation results indicate that volatility-normalized selection drives most of the variance reduction, while the covariance-aware projection provides an additional, consistent improvement. We further show that optional return-aware extensions can improve Sharpe ratios, and out-of-sample tests confirm that gains transfer to realized performance. CASP integrates as a drop-in replacement for Euclidean projection in metaheuristic portfolio optimizers. ...

Quantitative Financial Modeling for Sri Lankan Markets: Approach Combining NLP, Clustering and Time-Series Forecasting ArXiv ID: 2512.20216 “View on arXiv” Authors: Linuk Perera Abstract This research introduces a novel quantitative methodology tailored for quantitative finance applications, enabling banks, stockbrokers, and investors to predict economic regimes and market signals in emerging markets, specifically Sri Lankan stock indices (S&P SL20 and ASPI) by integrating Environmental, Social, and Governance (ESG) sentiment analysis with macroeconomic indicators and advanced time-series forecasting. Designed to leverage quantitative techniques for enhanced risk assessment, portfolio optimization, and trading strategies in volatile environments, the architecture employs FinBERT, a transformer-based NLP model, to extract sentiment from ESG texts, followed by unsupervised clustering (UMAP/HDBSCAN) to identify 5 latent ESG regimes, validated via PCA. These regimes are mapped to economic conditions using a dense neural network and gradient boosting classifier, achieving 84.04% training and 82.0% validation accuracy. Concurrently, time-series models (SRNN, MLP, LSTM, GRU) forecast daily closing prices, with GRU attaining an R-squared of 0.801 and LSTM delivering 52.78% directional accuracy on intraday data. A strong correlation between S&P SL20 and S&P 500, observed through moving average and volatility trend plots, further bolsters forecasting precision. A rule-based fusion logic merges ESG and time-series outputs for final market signals. By addressing literature gaps that overlook emerging markets and holistic integration, this quant-driven framework combines global correlations and local sentiment analysis to offer scalable, accurate tools for quantitative finance professionals navigating complex markets like Sri Lanka. ...

Unified Approach to Portfolio Optimization using the `Gain Probability Density Function’ and Applications ArXiv ID: 2512.11649 “View on arXiv” Authors: Jean-Patrick Mascomère, Jérémie Messud, Yagnik Chatterjee, Isabel Barros Garcia Abstract This article proposes a unified framework for portfolio optimization (PO), recognizing an object called the `gain probability density function (PDF)’ as the fundamental object of the problem from which any objective function could be derived. The gain PDF has the advantage of being 1-dimensional for any given portfolio and thus is easy to visualize and interpret. The framework allows us to naturally incorporate all existing approaches (Markowitz, CVaR-deviation, higher moments…) and represents an interesting basis to develop new approaches. It leads us to propose a method to directly match a target PDF defined by the portfolio manager, giving them maximal control on the PO problem and moving beyond approaches that focus only on expected return and risk. As an example, we develop an application involving a new objective function to control high profits, to be applied after a conventional PO (including expected return and risk criteria) and thus leading to sub-optimality w.r.t. the conventional objective function. We then propose a methodology to quantify a cost associated with this optimality deviation in a common budget unit, providing a meaningful information to portfolio managers. Numerical experiments considering portfolios with energy-producing assets illustrate our approach. The framework is flexible and can be applied to other sectors (financial assets, etc). ...

Reinforcement Learning in Financial Decision Making: A Systematic Review of Performance, Challenges, and Implementation Strategies ArXiv ID: 2512.10913 “View on arXiv” Authors: Mohammad Rezoanul Hoque, Md Meftahul Ferdaus, M. Kabir Hassan Abstract Reinforcement learning (RL) is an innovative approach to financial decision making, offering specialized solutions to complex investment problems where traditional methods fail. This review analyzes 167 articles from 2017–2025, focusing on market making, portfolio optimization, and algorithmic trading. It identifies key performance issues and challenges in RL for finance. Generally, RL offers advantages over traditional methods, particularly in market making. This study proposes a unified framework to address common concerns such as explainability, robustness, and deployment feasibility. Empirical evidence with synthetic data suggests that implementation quality and domain knowledge often outweigh algorithmic complexity. The study highlights the need for interpretable RL architectures for regulatory compliance, enhanced robustness in nonstationary environments, and standardized benchmarking protocols. Organizations should focus less on algorithm sophistication and more on market microstructure, regulatory constraints, and risk management in decision-making. ...

Exploratory Mean-Variance with Jumps: An Equilibrium Approach ArXiv ID: 2512.09224 “View on arXiv” Authors: Yuling Max Chen, Bin Li, David Saunders Abstract Revisiting the continuous-time Mean-Variance (MV) Portfolio Optimization problem, we model the market dynamics with a jump-diffusion process and apply Reinforcement Learning (RL) techniques to facilitate informed exploration within the control space. We recognize the time-inconsistency of the MV problem and adopt the time-inconsistent control (TIC) approach to analytically solve for an exploratory equilibrium investment policy, which is a Gaussian distribution centered on the equilibrium control of the classical MV problem. Our approach accounts for time-inconsistent preferences and actions, and our equilibrium policy is the best option an investor can take at any given time during the investment period. Moreover, we leverage the martingale properties of the equilibrium policy, design a RL model, and propose an Actor-Critic RL algorithm. All of our RL model parameters converge to the corresponding true values in a simulation study. Our numerical study on 24 years of real market data shows that the proposed RL model is profitable in 13 out of 14 tests, demonstrating its practical applicability in real world investment. ...

Portfolio Optimization via Transfer Learning ArXiv ID: 2511.21221 “View on arXiv” Authors: Kexin Wang, Xiaomeng Zhang, Xinyu Zhang Abstract Recognizing that asset markets generally exhibit shared informational characteristics, we develop a portfolio strategy based on transfer learning that leverages cross-market information to enhance the investment performance in the market of interest by forward validation. Our strategy asymptotically identifies and utilizes the informative datasets, selectively incorporating valid information while discarding the misleading information. This enables our strategy to achieve the maximum Sharpe ratio asymptotically. The promising performance is demonstrated by numerical studies and case studies of two portfolios: one consisting of stocks dual-listed in A-shares and H-shares, and another comprising equities from various industries of the United States. ...

Hybrid LSTM and PPO Networks for Dynamic Portfolio Optimization ArXiv ID: 2511.17963 “View on arXiv” Authors: Jun Kevin, Pujianto Yugopuspito Abstract This paper introduces a hybrid framework for portfolio optimization that fuses Long Short-Term Memory (LSTM) forecasting with a Proximal Policy Optimization (PPO) reinforcement learning strategy. The proposed system leverages the predictive power of deep recurrent networks to capture temporal dependencies, while the PPO agent adaptively refines portfolio allocations in continuous action spaces, allowing the system to anticipate trends while adjusting dynamically to market shifts. Using multi-asset datasets covering U.S. and Indonesian equities, U.S. Treasuries, and major cryptocurrencies from January 2018 to December 2024, the model is evaluated against several baselines, including equal-weight, index-style, and single-model variants (LSTM-only and PPO-only). The framework’s performance is benchmarked against equal-weighted, index-based, and single-model approaches (LSTM-only and PPO-only) using annualized return, volatility, Sharpe ratio, and maximum drawdown metrics, each adjusted for transaction costs. The results indicate that the hybrid architecture delivers higher returns and stronger resilience under non-stationary market regimes, suggesting its promise as a robust, AI-driven framework for dynamic portfolio optimization. ...

Reinforcement Learning for Portfolio Optimization with a Financial Goal and Defined Time Horizons ArXiv ID: 2511.18076 “View on arXiv” Authors: Fermat Leukam, Rock Stephane Koffi, Prudence Djagba Abstract This research proposes an enhancement to the innovative portfolio optimization approach using the G-Learning algorithm, combined with parametric optimization via the GIRL algorithm (G-learning approach to the setting of Inverse Reinforcement Learning) as presented by. The goal is to maximize portfolio value by a target date while minimizing the investor’s periodic contributions. Our model operates in a highly volatile market with a well-diversified portfolio, ensuring a low-risk level for the investor, and leverages reinforcement learning to dynamically adjust portfolio positions over time. Results show that we improved the Sharpe Ratio from 0.42, as suggested by recent studies using the same approach, to a value of 0.483 a notable achievement in highly volatile markets with diversified portfolios. The comparison between G-Learning and GIRL reveals that while GIRL optimizes the reward function parameters (e.g., lambda = 0.0012 compared to 0.002), its impact on portfolio performance remains marginal. This suggests that reinforcement learning methods, like G-Learning, already enable robust optimization. This research contributes to the growing development of reinforcement learning applications in financial decision-making, demonstrating that probabilistic learning algorithms can effectively align portfolio management strategies with investor needs. ...

Cryptocurrency Portfolio Management with Reinforcement Learning: Soft Actor–Critic and Deep Deterministic Policy Gradient Algorithms ArXiv ID: 2511.20678 “View on arXiv” Authors: Kamal Paykan Abstract This paper proposes a reinforcement learning–based framework for cryptocurrency portfolio management using the Soft Actor–Critic (SAC) and Deep Deterministic Policy Gradient (DDPG) algorithms. Traditional portfolio optimization methods often struggle to adapt to the highly volatile and nonlinear dynamics of cryptocurrency markets. To address this, we design an agent that learns continuous trading actions directly from historical market data through interaction with a simulated trading environment. The agent optimizes portfolio weights to maximize cumulative returns while minimizing downside risk and transaction costs. Experimental evaluations on multiple cryptocurrencies demonstrate that the SAC and DDPG agents outperform baseline strategies such as equal-weighted and mean–variance portfolios. The SAC algorithm, with its entropy-regularized objective, shows greater stability and robustness in noisy market conditions compared to DDPG. These results highlight the potential of deep reinforcement learning for adaptive and data-driven portfolio management in cryptocurrency markets. ...

Risk-Aware Deep Reinforcement Learning for Dynamic Portfolio Optimization ArXiv ID: 2511.11481 “View on arXiv” Authors: Emmanuel Lwele, Sabuni Emmanuel, Sitali Gabriel Sitali Abstract This paper presents a deep reinforcement learning (DRL) framework for dynamic portfolio optimization under market uncertainty and risk. The proposed model integrates a Sharpe ratio-based reward function with direct risk control mechanisms, including maximum drawdown and volatility constraints. Proximal Policy Optimization (PPO) is employed to learn adaptive asset allocation strategies over historical financial time series. Model performance is benchmarked against mean-variance and equal-weight portfolio strategies using backtesting on high-performing equities. Results indicate that the DRL agent stabilizes volatility successfully but suffers from degraded risk-adjusted returns due to over-conservative policy convergence, highlighting the challenge of balancing exploration, return maximization, and risk mitigation. The study underscores the need for improved reward shaping and hybrid risk-aware strategies to enhance the practical deployment of DRL-based portfolio allocation models. ...