Florentin Șerban

Cryptocurrency markets are characterized by elevated volatility, structural instability, and rapidly changing investor sentiment, which significantly challenge traditional portfolio optimization methodologies. Under such conditions, static portfolio allocation models frequently fail to ade-quately incorporate uncertainty, behavioral adaptation, and dynamic market responsiveness into the investment decision-making process. In parallel, recent advances in artificial intelligence and data-driven financial systems have transformed modern portfolio management by enabling adaptive investment strategies capable of processing large volumes of financial information in real time. Nevertheless, AI-assisted portfolio systems often remain highly sensitive to noisy market signals, parameter instability, and excessive portfolio rebalancing, particularly in volatile crypto-currency environments. This study proposes a behaviorally adaptive portfolio optimization framework under interval uncertainty that integrates robust optimization principles, behavioral finance mechanisms, non-linear transaction costs, and AI-assisted allocation adjustment within a unified cryptocurrency in-vestment structure. The proposed methodology introduces a behavioral preference parameter capable of dynamically adjusting portfolio composition according to varying investor attitudes toward uncertainty and market expectations. Simultaneously, interval uncertainty modeling is employed to represent ambiguous financial parameters through bounded intervals, while artificial intelligence mechanisms act as adaptive decision-support tools that improve portfolio respon-siveness under changing market conditions. The empirical analysis is conducted using major cryptocurrency assets, including Bitcoin, Ethereum, Solana, and Binance Coin, over the period January–June 2025. Multiple behavioral portfolio configurations are evaluated in order to analyze the interaction between profitability, downside risk, portfolio stability, and transaction cost efficiency. The results indicate that the proposed framework improves risk-adjusted portfolio performance and generates more stable allocation strategies compared to traditional static portfolio optimization approaches. In particular, the integration of behavioral adaptation and robust optimization contributes to reduced sensitivity to estimation uncertainty and unstable market fluctuations. The findings further demonstrate that AI-assisted adaptive allocation mechanisms improve portfolio flexibility and support smoother portfolio transitions under volatile market conditions. Moreover, the incorporation of nonlinear transaction costs leads to more realistic and practically implementable cryptocurrency investment strategies. Overall, the proposed framework provides a robust and behaviorally interpretable approach for modern cryptocurrency portfolio management and contributes to the growing literature at the intersection of artificial intelligence, behavioral fi-nance, and uncertainty-aware portfolio optimization.

Modern financial markets are increasingly shaped by algorithmic trading systems and artificial intelligence techniques that process large volumes of financial data in real time. However, machine learning-based trading systems often suffer from signal instability and excessive sensitivity to market noise, which may lead to overtrading and increased financial risk. In highly volatile environments such as cryptocurrency markets, the reliability of trading signals becomes a critical issue for both portfolio allocation and risk management. This study proposes an entropy-filtered machine learning framework designed to enhance the stability and risk-awareness of algorithmic trading strategies. The proposed approach integrates entropy-based filtering techniques with machine learning classifiers in order to reduce noise in market signals, thereby improving the risk-adjusted stability of trading strategies. Entropy measures are employed as a filtering mechanism that evaluates the informational content of predictive signals and suppresses unreliable model outputs. The empirical analysis is conducted using cryptocurrency market data, where the entropy-filtered framework is applied to trading signal generation and decision making. The results indicate that the proposed approach improves the stability of trading signals and reduces the occurrence of false signals compared to conventional machine learning models. In addition, entropy filtering contributes to a more balanced risk–return profile and enhances the overall robustness of trading strategies. Moreover, entropy filtering contributes to a more balanced risk–return profile and enhances the overall robustness of trading strategies. The findings suggest that entropy-based filtering substantially improves the reliability and risk-awareness of machine learning trading systems, providing a promising direction for the development of more robust AI-driven financial decision frameworks.

Modern financial markets are increasingly shaped by algorithmic trading systems and artificial intelligence techniques that process large volumes of financial data in real time. However, machine learning–based trading systems often suffer from signal instability and excessive sensitivity to market noise, which may lead to overtrading and increased financial risk. In highly volatile environments such as cryptocurrency markets, the re-liability of trading signals becomes a critical issue for both portfolio allocation and risk management. This study proposes an entropy-filtered machine learning framework designed to en-hance the stability and risk-awareness of algorithmic trading strategies. The proposed approach integrates entropy-based filtering techniques with machine learning classifiers in order to reduce noise in market signals improving the risk-adjusted stability of algo-rithmic trading strategies. Entropy measures are employed as a filtering mechanism that evaluates the informational content of market signals and suppresses unreliable predic-tions generated by the learning model. The empirical analysis is conducted using cryp-tocurrency market data, where the entropy-filtered machine learning framework is ap-plied to trading signal generation and portfolio decision making. The results indicate that the proposed approach improves the stability of trading signals and reduces the occur-rence of false signals compared to conventional machine learning trading models. Moreover, the integration of entropy filtering contributes to a more balanced risk–return profile and enhances the overall robustness of algorithmic trading strategies.The findings suggest that combining information-theoretic measures with machine learning tech-niques represents a promising direction for developing more reliable and risk-aware financial decision systems. The results suggest that entropy-based filtering can substan-tially improve the robustness and risk-awareness of machine learning trading systems, providing a promising direction for future AI-driven financial decision frameworks.

Traditional mean–variance portfolio optimization proves inadequate for cryptocurrency markets, where extreme volatility, fat-tailed return distributions, and unstable correlation structures undermine the validity of variance as a comprehensive risk measure. To address these limitations, this paper proposes a unified entropy-based portfolio optimization framework grounded in the Maximum Entropy Principle (MaxEnt). Within this setting, Shannon entropy, Tsallis entropy, and Weighted Shannon Entropy (WSE) are formally derived as particular specifications of a common constrained optimization problem solved via the method of Lagrange multipliers, ensuring analytical coherence and mathematical transparency. Moreover, the proposed MaxEnt formulation provides an information-theoretic interpretation of portfolio diversification as an inference problem under uncertainty, where optimal allocations correspond to the least informative distributions consistent with prescribed moment constraints. In this perspective, entropy acts as a structural regularizer that governs the geometry of diversification rather than as a direct proxy for risk. This interpretation strengthens the conceptual link between entropy, uncertainty quantification, and decision-making in complex financial systems, offering a robust and distribution-free alternative to classical variance-based portfolio optimization. The proposed framework is empirically illustrated using a portfolio composed of major cryptocurrencies—Bitcoin (BTC), Ethereum (ETH), Solana (SOL), and Binance Coin (BNB)—based on weekly return data. The results reveal systematic differences in the diversification behavior induced by each entropy measure: Shannon entropy favors near-uniform allocations, Tsallis entropy imposes stronger penalties on concentration and enhances robustness to tail risk, while WSE enables the incorporation of asset-specific informational weights reflecting heterogeneous market characteristics. From a theoretical perspective, the paper contributes a coherent MaxEnt formulation that unifies several entropy measures within a single information-theoretic optimization framework, clarifying the role of entropy as a structural regularizer of diversification. From an applied standpoint, the results indicate that entropy-based criteria yield stable and interpretable allocations across turbulent market regimes, offering a flexible alternative to classical risk-based portfolio construction. The framework naturally extends to dynamic multi-period settings and alternative entropy formulations, providing a foundation for future research on robust portfolio optimization under uncertainty.

Traditional mean–variance portfolio optimization proves inadequate for cryptocurrency markets, where extreme volatility, fat-tailed return distributions, and unstable correlation structures undermine the validity of variance as a comprehensive risk measure. To address these limitations, this paper proposes a unified entropy-based portfolio optimization framework grounded in the Maximum Entropy Principle (MaxEnt). Within this setting, Shannon entropy, Tsallis entropy, and Weighted Shannon Entropy (WSE) are formally derived as particular specifications of a common constrained optimization problem solved via the method of Lagrange multipliers, ensuring analytical coherence and mathematical transparency. Moreover, the proposed MaxEnt formulation provides an information-theoretic interpretation of portfolio diversification as an inference problem under uncertainty, where optimal allocations correspond to the least informative distributions consistent with prescribed moment constraints. In this perspective, entropy acts as a structural regularizer that governs the geometry of diversification rather than as a direct proxy for risk. This interpretation strengthens the conceptual link between entropy, uncertainty quantification, and decision-making in complex financial systems, offering a robust and distribution-free alternative to classical variance-based portfolio optimization. The proposed framework is empirically illustrated using a portfolio composed of major cryptocurrencies—Bitcoin (BTC), Ethereum (ETH), Solana (SOL), and Binance Coin (BNB)—based on weekly return data. The results reveal systematic differences in the diversification behavior induced by each entropy measure: Shannon entropy favors near-uniform allocations, Tsallis entropy imposes stronger penalties on concentration and enhances robustness to tail risk, while WSE enables the incorporation of asset-specific informational weights reflecting heterogeneous market characteristics. From a theoretical perspective, the paper contributes a coherent MaxEnt formulation that unifies several entropy measures within a single information-theoretic optimization framework, clarifying the role of entropy as a structural regularizer of diversification. From an applied standpoint, the results indicate that entropy-based criteria yield stable and interpretable allocations across turbulent market regimes, offering a flexible alternative to classical risk-based portfolio construction. The framework naturally extends to dynamic multi-period settings and alternative entropy formulations, providing a foundation for future research on robust portfolio optimization under uncertainty.

This paper develops a robust portfolio optimization framework that integrates Weighted Shannon Entropy (WSE) into the classical mean–variance paradigm, offering a distribution-free approach to diversification suited for volatile and heavy-tailed markets. While traditional variance-based models are highly sensitive to estimation errors and instability in covariance structures—issues that are particularly acute in cryptocurrency markets—entropy provides a structural mechanism for mitigating concentration risk and enhancing resilience under uncertainty. By incorporating informational weights that reflect asset-specific characteristics such as volatility, market capitalization, and liquidity, the WSE model generalizes classical Shannon entropy and allows for more realistic, data-driven diversification profiles. Analytical solutions derived from the maximum entropy principle and Lagrange multipliers yield exponential-form portfolio weights that balance expected return, variance, and diversification. The empirical analysis examines two case studies: a four-asset cryptocurrency portfolio (BTC, ETH, SOL, and BNB) over January–March 2025, and an extended twelve-asset portfolio over April 2024–March 2025 with rolling rebalancing and proportional transaction costs. The results show that WSE portfolios achieve systematically higher entropy scores, more balanced allocations, and improved downside protection relative to both equal-weight and classical mean–variance portfolios. Risk-adjusted metrics confirm these improvements: WSE delivers higher Sharpe ratios and less negative Conditional Value-at-Risk (CVaR), together with reduced overexposure to highly volatile assets. Overall, the findings demonstrate that Weighted Shannon Entropy offers a transparent, flexible, and robust framework for portfolio construction in environments characterized by nonlinear dependencies, structural breaks, and parameter uncertainty. Beyond its empirical performance, the WSE model provides a theoretically grounded bridge between information theory and risk management, with strong potential for applications in algorithmic allocation, index construction, and regulatory settings where diversification and stability are essential. Moreover, the integration of informational weighting schemes highlights the capacity of WSE to incorporate both statistical properties and market microstructure signals, thereby enhancing its practical relevance for real-world investment decision-making.

Traditional mean–variance portfolio optimization is ill-suited to cryptocurrency markets, where extreme volatility, fat-tailed distributions, and unstable correlations undermine variance as a risk measure. To overcome these limitations, this paper develops a unified entropy-based framework for portfolio diversification grounded in the Maximum Entropy Principle (MaxEnt). Within this formulation, Shannon entropy, Tsallis entropy, and Weighted Shannon Entropy (WSE) emerge as complementary specifications derived analytically via the method of Lagrange multipliers, ensuring mathematical tractability and interpretability. Empirical validation is conducted on a portfolio of four leading cryptocurrencies—Bitcoin (BTC), Ethereum (ETH), Solana (SOL), and Binance Coin (BNB)—using weekly return data from January to March 2025. Results reveal that Shannon entropy converges to near-uniform diversification, Tsallis entropy (q = 2) penalizes concentration more strongly and enhances robustness against tail risk, while WSE integrates asset-specific informational priorities, aligning allocations with investor preferences or market characteristics. Comparative analysis confirms that all three models yield allocations more resilient and structurally balanced than variance-driven portfolios, mitigating estimation risk and concentration effects. This study provides a coherent mathematical formulation of entropy-based portfolio optimization by embedding Shannon, Tsallis, and Weighted Shannon entropies within a common Maximum Entropy (MaxEnt) optimization framework. Beyond its immediate empirical scope, this work also opens several avenues for future research. First, entropy-based portfolio construction can be extended to dynamic multi-period settings with transaction costs and liquidity frictions, which are particularly relevant in cryptocurrency markets. Second, the framework may be generalized to incorporate alternative entropy measures such as Rényi or Kaniadakis entropy, enabling more refined sensitivity to tail risks and nonlinear dependencies. The proposed framework provides a flexible foundation for future extensions toward dynamic, multi-period portfolio optimization under uncertainty.

Portfolio optimization is a cornerstone of modern financial decision-making, traditionally based on the mean–variance model introduced by Markowitz. However, this framework relies on restrictive assumptions—such as normally distributed returns and symmetric risk preferences—that often fail in real-world markets, particularly in volatile and non-Gaussian environments such as cryptocurrencies. To address these limitations, this paper proposes a novel multi-objective model that combines expected return maximization, mean absolute deviation (MAD) minimization, and entropy-based diversification into a unified optimization structure: the Mean–Deviation–Entropy (MDE) model. The MAD metric offers a robust alternative to variance by capturing the average magnitude of deviations from the mean without inflating extreme values, while entropy serves as an information-theoretic proxy for portfolio diversification and uncertainty. Three entropy formulations are considered—Shannon entropy, Tsallis entropy, and cumulative residual Sharma–Taneja–Mittal entropy (CR-STME)—to explore different notions of uncertainty and structural diversity. The MDE model is formulated as a tri-objective optimization problem and solved via scalarization techniques, enabling flexible trade-offs between return, deviation, and entropy. The framework is empirically tested on a cryptocurrency portfolio composed of Bitcoin (BTC), Ethereum (ETH), Solana (SOL), and Binance Coin (BNB), using daily data over a 12-month period. The empirical setting reflects a high-volatility, high-skewness regime, ideal for testing entropy-driven diversification. Comparative outcomes reveal that entropy-integrated models yield more robust weightings, particularly when tail risk and regime shifts are present. Comparative results against classical mean–variance and mean–MAD models indicate that the MDE model achieves improved diversification, enhanced allocation stability, and greater resilience to volatility clustering and tail risk. This study contributes to the literature on robust portfolio optimization by integrating entropy as a formal objective within a scalarized multi-criteria framework. The proposed approach offers promising applications in sustainable investing, algorithmic asset allocation, and decentralized finance, especially under high-uncertainty market conditions.

Portfolio optimization is a cornerstone of modern financial decision-making, tradition-ally based on the mean–variance model introduced by Markowitz. However, this framework relies on restrictive assumptions—such as normally distributed returns and symmetric risk preferences—that often fail in real-world markets, particularly in volatile and non-Gaussian environments such as cryptocurrencies. To address these limitations, this paper proposes a novel multi-objective model that combines expected return max-imization, mean absolute deviation (MAD) minimization, and entropy-based diversifi-cation into a unified optimization structure: the Mean–Deviation–Entropy (MDE) model. The MAD metric offers a robust alternative to variance by capturing the average mag-nitude of deviations from the mean without inflating extreme values, while entropy serves as an information-theoretic proxy for portfolio diversification and uncertainty. Three entropy formulations are considered—Shannon entropy, Tsallis entropy, and cumulative residual Sharma–Taneja–Mittal entropy (CR-STME)—to explore different notions of uncertainty and structural diversity. The MDE model is formulated as a tri-objective optimization problem and solved via scalarization techniques, enabling flexible trade-offs between return, deviation, and en-tropy. The framework is empirically tested on a cryptocurrency portfolio composed of Bitcoin (BTC), Ethereum (ETH), Solana (SOL), and Binance Coin (BNB), using daily data over a 12-month period. The empirical setting reflects a high-volatility, high-skewness regime, ideal for testing entropy-driven diversification. Comparative outcomes reveal that entropy-integrated models yield more robust weightings, particularly when tail risk and regime shifts are present. Comparative results against classical mean–variance and mean–MAD models indicate that the MDE model achieves improved di-versification, enhanced allocation stability, and greater resilience to volatility clustering and tail risk. This study contributes to the literature on robust portfolio optimization by integrating entropy as a formal objective within a scalarized multi-criteria framework. The proposed approach offers promising applications in sustainable investing, algorithmic asset allo-cation, and decentralized finance, especially under high-uncertainty market conditions.

In this paper, we propose a novel optimization model for portfolio selection that integrates the classical mean–variance criterion with a second-order Tsallis entropy term. This approach enables a trade-off between expected return, risk, and diversification, extending Markowitz’s theory to account for non-Gaussian characteristics and heavy-tailed distributions that are typical in financial markets—especially in cryptocurrency assets. Unlike the first-order Tsallis entropy, the second-order version amplifies the effects of distributional structure and allows for more refined penalization of portfolio concentration. We derive the analytical solution for the optimal weights under this extended framework and demonstrate its performance through a case study using real data from selected cryptocurrencies. Efficient frontiers, portfolio weights, and entropy indicators are compared across models. This novel combination may improve portfolio selection under uncertainty, especially in the context of volatile assets such as cryptocurrencies, as the proposed model can provide a more robust and diversified portfolio structure compared to conventional theories.