Portfolio

Black-Litterman and ESG Portfolio Optimization ArXiv ID: 2511.21850 “View on arXiv” Authors: Aviv Alpern, Svetlozar Rachev Abstract We introduce a simple portfolio optimization strategy using ESG data with the Black-Litterman allocation framework. ESG scores are used as a bias for Stein shrinkage estimation of equilibrium risk premiums used in assigning Black-Litterman asset weights. Assets are modeled as multivariate affine normal-inverse Gaussian variables using CVaR as a risk measure. This strategy, though very simple, when employed with a soft turnover constraint is exceptionally successful. Portfolios are reallocated daily over a 4.7 year period, each with a different set of hyperparameters used for optimization. The most successful strategies have returns of approximately 40-45% annually. ...

Informative Risk Measures in the Banking Industry: A Proposal based on the Magnitude-Propensity Approach ArXiv ID: 2511.21556 “View on arXiv” Authors: Michele Bonollo, Martino Grasselli, Gianmarco Mori, Havva Nilsu Oz Abstract Despite decades of research in risk management, most of the literature has focused on scalar risk measures (like e.g. Value-at-Risk and Expected Shortfall). While such scalar measures provide compact and tractable summaries, they provide a poor informative value as they miss the intrinsic multivariate nature of risk.To contribute to a paradigmatic enhancement, and building on recent theoretical work by Faugeras and Pagés (2024), we propose a novel multivariate representation of risk that better reflects the structure of potential portfolio losses, while maintaining desirable properties of interpretability and analytical coherence. The proposed framework extends the classical frequency-severity approach and provides a more comprehensive characterization of extreme events. Several empirical applications based on real-world data demonstrate the feasibility, robustness and practical relevance of the methodology, suggesting its potential for both regulatory and managerial applications. ...

Carbon-Penalised Portfolio Insurance Strategies in a Stochastic Factor Model with Partial Information ArXiv ID: 2511.19186 “View on arXiv” Authors: Katia Colaneri, Federico D’Amario, Daniele Mancinelli Abstract Given the increasing importance of environmental, social and governance (ESG) factors, particularly carbon emissions, we investigate optimal proportional portfolio insurance (PPI) strategies accounting for carbon footprint reduction. PPI strategies enable investors to mitigate downside risk while retaining the potential for upside gains. This paper aims to determine the multiplier of the PPI strategy to maximise the expected utility of the terminal cushion, where the terminal cushion is penalised proportionally to the realised volatility of stocks issued by firms operating in carbon-intensive sectors. We model the risky assets’ dynamics using geometric Brownian motions whose drift rates are modulated by an unobservable common stochastic factor to capture market-specific or economy-wide state variables that are typically not directly observable. Using classical stochastic filtering theory, we formulate a suitable optimization problem and solve it for CRRA utility function. We characterise optimal carbon penalised PPI strategies and optimal value functions under full and partial information and quantify the loss of utility due incomplete information. Finally, we carry a numerical analysis showing that the proposed strategy reduces carbon emission intensity without compromising financial performance. ...

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. ...

(Non-Parametric) Bootstrap Robust Optimization for Portfolios and Trading Strategies ArXiv ID: 2510.12725 “View on arXiv” Authors: Daniel Cunha Oliveira, Grover Guzman, Nick Firoozye Abstract Robust optimization provides a principled framework for decision-making under uncertainty, with broad applications in finance, engineering, and operations research. In portfolio optimization, uncertainty in expected returns and covariances demands methods that mitigate estimation error, parameter instability, and model misspecification. Traditional approaches, including parametric, bootstrap-based, and Bayesian methods, enhance stability by relying on confidence intervals or probabilistic priors but often impose restrictive assumptions. This study introduces a non-parametric bootstrap framework for robust optimization in financial decision-making. By resampling empirical data, the framework constructs flexible, data-driven confidence intervals without assuming specific distributional forms, thus capturing uncertainty in statistical estimates, model parameters, and utility functions. Treating utility as a random variable enables percentile-based optimization, naturally suited for risk-sensitive and worst-case decision-making. The approach aligns with recent advances in robust optimization, reinforcement learning, and risk-aware control, offering a unified perspective on robustness and generalization. Empirically, the framework mitigates overfitting and selection bias in trading strategy optimization and improves generalization in portfolio allocation. Results across portfolio and time-series momentum experiments demonstrate that the proposed method delivers smoother, more stable out-of-sample performance, offering a practical, distribution-free alternative to traditional robust optimization methods. ...

Periodic portfolio selection with quasi-hyperbolic discounting ArXiv ID: 2410.18240 “View on arXiv” Authors: Unknown Abstract We introduce an infinite-horizon, continuous-time portfolio selection problem faced by an agent with periodic S-shaped preference and present bias. The inclusion of a quasi-hyperbolic discount function leads to time-inconsistency and we characterize the optimal portfolio for a pre-committing, naive and sophisticated agent respectively. In the more theoretically challenging problem with a sophisticated agent, the time-consistent planning strategy can be formulated as an equilibrium to a static mean field game. Interestingly, present bias and naivety do not necessarily result in less desirable risk taking behaviors, while agent’s sophistication may lead to excessive leverage (underinvestement) in the bad (good) states of the world. ...