Portfolio optimization is a fundamental problem in financial theory, aiming to balance risk and return in asset allocation. Traditional models, such as Mean–Variance optimization, are effective, but often fail to account for diversification adequately. This study introduces the Mean–Variance–Entropy (MVE) model, which integrates Tsallis entropy into the classic Mean–Variance framework to enhance portfolio diversification and risk management. Entropy, specifically second-order entropy, penalizes excessive concentration in the portfolio, encouraging a more balanced and diversified allocation of assets. The model is applied to a portfolio of five major cryptocurrencies: Bitcoin (BTC), Ethereum (ETH), Solana (SOL), Cardano (ADA), and Binance Coin (BNB). The performance of the MVE model is compared with that of the traditional Mean–Variance model, and results demonstrate that the entropy-enhanced model provides better diversification, although with a slightly lower Sharpe ratio. The findings suggest that while the entropy-adjusted model results in a slightly lower Sharpe ratio, it offers better diversification and a more resilient portfolio, especially in volatile markets. This study demonstrates the potential of incorporating entropy into portfolio optimization as a means to mitigate concentration risk and improve portfolio performance. The approach is particularly beneficial for markets such as cryptocurrency, where volatility and asset correlations fluctuate rapidly. This paper contributes to the growing body of literature on portfolio optimization by offering a more diversified, robust, and risk-adjusted approach to asset allocation

This study investigates post-crisis digital transformation and business model adaptation in Eastern Europe and the Middle East, regions with diverse economic structures and varying technological maturity. It explores how organizations in these regions utilized digital technologies to navigate crisis conditions, focusing on the interplay between digital agility, data-driven strategies, and business sustainability. Existing literature emphasizes the growing importance of digital transformation for organizational resilience, particularly during disruptions. However, the specific challenges and opportunities within emerging economies like those in Eastern Europe and the Middle East remain underexplored. This research addresses this gap by examining how digital agility influences business sustainability post-crisis, whether digital transformation effectiveness varies across sectors, and what key drivers and barriers exist for successful digital transformation in these regions. Key findings reveal a strong positive correlation between digital agility and post-crisis business sustainability; significant sectoral variations in digital transformation success, with financial services and healthcare leading; regional differences in digital adoption and effectiveness, with Middle Eastern companies demonstrating higher efficiency gains despite structural barriers; the importance of integrating digital strategies beyond operational efficiency for sustained growth; and crucial roles for leadership, digital governance, employee training, external partnerships, cloud computing, and AI, while common barriers include implementation costs, workforce resistance, and cybersecurity concerns. These findings contribute empirical evidence of the link between digital transformation and post-crisis resilience in emerging economies. The study highlights the importance of a holistic approach, encompassing not only technology but also strategic alignment, leadership, human capital, and customer-centricity. It underscores the need for enabling policy environments, including infrastructure investment, SME support, and robust cybersecurity frameworks. Limitations include geographical focus and sample size. Future research could explore long-term digital sustainability, emerging technology impacts, and sector-specific challenges.

This research investigates the transformative influence of Fintech on reshaping business models within the dynamic context of Eastern Europe and the Middle East (EEME) in the post-COVID-19 era. The study examines how the pandemic has accelerated Fintech adoption and its subsequent impact on business model evolution across various sectors in the region. Existing literature highlights the disruptive potential of Fintech globally, but there is a gap in understanding its specific impact on the EEME region, particularly in the post-pandemic recovery phase. This study addresses this gap by exploring the complex interplay between Fintech adoption and business model transformation. A large-scale survey of 1050 businesses operating in various sectors across EEME was conducted. The survey captured data on Fintech adoption rates, types of solutions utilized, changes in key aspects of business models (revenue generation, customer acquisition, operations, value proposition), enabling factors (regulatory support, consumer demand, digital infrastructure), and perceived challenges (cybersecurity, data privacy). Statistical analysis, including correlation and regression analysis, was employed to test the research hypotheses. The findings reveal a significant acceleration of Fintech adoption post-COVID-19, with 78% of businesses adopting new Fintech solutions compared to 32% pre-pandemic. Key drivers of adoption include regulatory support for digital finance (β = 0.62, p < 0.001), consumer demand for digital services (β = 0.55, p < 0.001), and digital infrastructure development (β = 0.48, p < 0.001). Sectoral variations in impact were observed, with finance (85% reporting significant changes) and retail (72%) experiencing greater transformation than manufacturing (48%). While cybersecurity and data privacy concerns were prevalent (68% and 55% respectively), their negative correlation with business model transformation was relatively weak (β = -0.25 and β = -0.20, p < 0.05). These results suggest that while challenges exist, they do not necessarily prevent businesses from adapting their models using Fintech. This study contributes to the field by providing empirical evidence of the transformative role of Fintech in EEME post-COVID-19, highlighting the key drivers and challenges, and revealing sectoral variations in impact. The findings have practical implications for businesses, policymakers, and investors in the region. The research acknowledges limitations inherent in survey-based methodologies, such as potential response bias and the cross-sectional nature of the data, which limits causal inferences. Future research could explore these dynamics through longitudinal studies and qualitative investigations.

Traditional portfolio optimization models primarily focus on two key elements: risk and return. In this study, we extend this classical framework by introducing a third critical dimension—liquidity. We propose a novel model in mean–risk–liquidity framework that incorporate second-order entropy into the Markowitz portfolio theory. Our models assign flexible weights based on the investor’s preferences regarding return and entropy, highlighting the role of diversification as a potential enhancer of liquidity. Building on this approach, we derive analytical expressions that offer concrete solutions to the portfolio optimization problem. Computational results validating our models are presented and comments in the final.

This study explores the use of Shannon entropy as a filtering mechanism to enhance the trading signals produced by the LVQ (Learning Vector Quantization) machine learning algorithm in algorithmic trading. The integration of Shannon entropy aims to improve trade entry accuracy by reducing market noise and identifying stronger trends. A trading bot was developed and tested on Bitcoin using a three-minute timeframe on the TradingView platform, with backtesting conducted from February 1 to February 18, 2025. The fully automated strategy used 100% of available capital per trade, reinvesting profits for compounding. Positions were closed when an opposite signal was generated. A comparative analysis revealed that incorporating Shannon entropy outperformed a baseline strategy. These findings demonstrate that entropy-based filtering improves trade selection and profitability by reducing market noise and focusing on reliable trends, suggesting its potential for broader application in algorithmic trading.

The rapid development of cryptocurrency markets has intensified the use of algorithmic trading systems capable of operating under high volatility and non-stationary market conditions. In this context, machine learning–based trading bots have gained increasing attention due to their potential to adapt dynamically to evolving price patterns. This study investigates the performance of two supervised machine learning classification approaches—k-Nearest Neighbors (kNN) and Learning Vector Quantization (LVQ)—when applied to automated trading in the Bitcoin market. The research addresses the following question: Do adaptive prototype-based learning models outperform instance-based classification models in algorithmic trading applications under identical market conditions? To answer this question, two fully automated trading bots were developed by the authors and implemented on the TradingView platform using Pine Script. Both bots were evaluated under identical experimental settings, trading the BTC/USDT pair on an hourly time frame over the period January 2025 to January 2026, with an initial capital of 1000 USD. Additional market strength and trend filters were applied to enhance signal robustness. The empirical results reveal notable differences between the two learning paradigms. The kNN-based trading bot exhibited a conservative trading behavior, characterized by lower trade frequency and moderate drawdown, but failed to generate positive cumulative returns. In contrast, the LVQ-based trading bot achieved superior profitability and demonstrated a stronger capacity to adapt to changing market regimes, albeit at the cost of significantly higher drawdown and increased risk exposure. The findings suggest that adaptive prototype-based learning models such as LVQ are better suited for algorithmic trading in highly volatile cryptocurrency markets when profitability and adaptability are prioritized. However, the increased risk associated with such models highlights the importance of incorporating robust risk management mechanisms. Overall, this study contributes to the literature by providing a controlled, implementation-level comparison of two machine learning trading strategies using realistic market conditions and fully automated trading systems.