Sign in to use this feature.

Years

Between: -

Subjects

remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline

Journals

Article Types

Countries / Regions

Search Results (55)

Search Parameters:
Keywords = robust asset allocation

Order results
Result details
Results per page
Select all
Export citation of selected articles as:
16 pages, 1800 KB  
Article
Navigating Extreme Market Fluctuations: Asset Allocation Strategies in Developed vs. Emerging Economies
by Lumengo Bonga-Bonga
Econometrics 2026, 14(1), 16; https://doi.org/10.3390/econometrics14010016 - 17 Mar 2026
Viewed by 192
Abstract
This paper examines how assets from emerging and developed stock markets can be efficiently allocated during periods of financial crisis by integrating traditional portfolio theory with Extreme Value Theory (EVT), using the Generalized Pareto Distribution (GPD) and Generalized Extreme Value (GEV) approaches to [...] Read more.
This paper examines how assets from emerging and developed stock markets can be efficiently allocated during periods of financial crisis by integrating traditional portfolio theory with Extreme Value Theory (EVT), using the Generalized Pareto Distribution (GPD) and Generalized Extreme Value (GEV) approaches to model tail risks. This study evaluates mean-variance portfolios constructed under each EVT framework and finds that portfolios based on GPD estimates consistently favour emerging market assets, which outperform both developed market and internationally diversified portfolios during extreme market conditions. In contrast, GEV-based portfolios indicate superior performance for developed market assets, highlighting the distinct behaviour of returns in the upper and lower tails of the distribution. These contrasting results reveal the unique nature of safe-haven characteristics associated with developed economies, the assets of which demonstrate greater stability and resilience during episodes of financial stress. By showing how tail-risk modelling alters optimal portfolio weights across market types, this paper contributes new evidence to the literature on crisis-informed asset allocation and offers practical insights for investors seeking robust diversification strategies under extreme market fluctuations. Full article
Show Figures

Figure 1

32 pages, 1008 KB  
Article
Transfer Pricing and Macroeconomic Stability: A Multi-Country Analysis of European Economies
by Mohammed Amine Hajjaj, Zakariae Bel Mkaddem, Hicham Es-Saadi, Imane Tesse and Jihane Chahib
J. Risk Financial Manag. 2026, 19(3), 218; https://doi.org/10.3390/jrfm19030218 - 16 Mar 2026
Viewed by 310
Abstract
Transfer pricing has become a major channel through which multinational enterprises shift profits across countries. This study examines the macroeconomic and institutional determinants of transfer pricing in seven European economies (France, Spain, Germany, the United Kingdom, Italy, the Netherlands, and Portugal) over the [...] Read more.
Transfer pricing has become a major channel through which multinational enterprises shift profits across countries. This study examines the macroeconomic and institutional determinants of transfer pricing in seven European economies (France, Spain, Germany, the United Kingdom, Italy, the Netherlands, and Portugal) over the period 1985–2025. The main objective is to identify the key factors influencing profit shifting and to analyze the mechanisms through which multinational firms allocate profits across jurisdictions. The study employs panel data techniques and uses two different proxies to capture transfer pricing practices (trade-based and intangible-based channels). To analyze both long-run and short-run relationships between transfer pricing, exchange rate dynamics, foreign direct investment, inflation and institutional quality, the analysis relies on heterogeneous panel estimators and cointegration tests, supported by several robustness checks. The empirical results reveal the existence of a long-run relationship between transfer pricing and its macroeconomic and institutional determinants. Exchange rate fluctuations and inflation exert a negative effect on transfer pricing, whereas Foreign Direct Investment has a positive impact by expanding multinational investment networks and intra-group transactions. The effect of institutional quality, proxied by control of corruption, appears more heterogeneous and may vary across jurisdictions as well as across the type of transfer pricing channel, whether related to tangible trade or intangible assets. These results emphasize the importance of institutional quality and international tax coordination in limiting aggressive profit-shifting practices. Full article
(This article belongs to the Section Economics and Finance)
Show Figures

Figure 1

33 pages, 1613 KB  
Article
Forecasting Risk Matrices with Economic Policy Uncertainty and Financial Stress: A Machine Learning Approach
by Jinda Du, Wenyi Cao and Ziyou Wang
Mathematics 2026, 14(6), 938; https://doi.org/10.3390/math14060938 - 10 Mar 2026
Viewed by 471
Abstract
Accurately forecasting the risk matrix and constructing a well-controlled portfolio based on these forecasts is the core objective of effective asset allocation. This paper takes the Chinese stock market as the research object, employing multiple machine learning algorithms to systematically compare the predictive [...] Read more.
Accurately forecasting the risk matrix and constructing a well-controlled portfolio based on these forecasts is the core objective of effective asset allocation. This paper takes the Chinese stock market as the research object, employing multiple machine learning algorithms to systematically compare the predictive performance of the Financial Stress (FS) indicator and the Economic Policy Uncertainty (EPU) index in sectoral risk management. The forecast results are subsequently applied to portfolio construction and optimization. The findings indicate that, in terms of predictive dimensions, EPU demonstrates strong performance in short-term forecasts, but its explanatory power decays rapidly as the forecasting horizon extends. In contrast, the FS factor achieves forecasting accuracy that is significantly superior to both the EPU factor and traditional price series across all time horizons, exhibiting robust long-memory characteristics and cross-period stability. At the portfolio application level, the minimum variance strategy constructed based on FS forecasts effectively reduces out-of-sample portfolio variance, achieving superior risk control performance compared to strategies based on EPU factor forecasts. This result reveals the differentiated mechanisms of the two factor types: EPU acts as a driving force for short-term risk structure reshaping, while financial stress serves as the core variable driving the evolution of long-term risk structures. Machine learning methods provide an effective technical pathway for capturing these complex nonlinear relationships. The research conclusions offer new empirical evidence for investors to optimize asset allocation decisions and for regulatory authorities to improve risk monitoring systems. Full article
Show Figures

Figure 1

23 pages, 2631 KB  
Article
A Novel Portfolio Selection Method via Deep Reinforcement Learning
by Ni Gao, Yan Liu, Yiyue He, Juan Zhang and Lefang Zhang
Systems 2026, 14(3), 292; https://doi.org/10.3390/systems14030292 - 9 Mar 2026
Viewed by 298
Abstract
Portfolio selection is a fundamental task in quantitative finance that aims to allocate capital across assets to balance risk and return. While deep learning has shown great promise in this field, extracting reliable feature representations from non-stationary and noisy financial data remains a [...] Read more.
Portfolio selection is a fundamental task in quantitative finance that aims to allocate capital across assets to balance risk and return. While deep learning has shown great promise in this field, extracting reliable feature representations from non-stationary and noisy financial data remains a significant challenge. The existing models often fail to simultaneously capture the temporal dynamics of price series and complex inter-asset correlations, which limits their trading performance. To address these issues, we propose Denoising-Sequence-Correlation Reinforcement Learning (DSCRL), a novel portfolio selection framework based on deep reinforcement learning. DSCRL employs a dual-stream feature extraction network, where one stream aims to learn temporal market dynamics and the other aims to capture asset correlations, enabling more informative representations. A denoising module is further integrated to mitigate the impact of noise, ensuring stability and robustness in the learning process. Furthermore, a deterministic policy gradient (DPG)-based decision network is designed to directly optimize continuous portfolio weights and normalize them to satisfy budget constraints while preserving the importance. Extensive experiments conducted on multiple benchmark datasets demonstrate that DSCRL consistently outperforms both traditional financial heuristics and advanced deep reinforcement approaches. The results highlight its superior ability to achieve higher cumulative returns with lower volatility. Overall, DSCRL provides an effective and robust solution that strikes a better trade-off between pursuing profits and managing risks in dynamic financial markets. Full article
Show Figures

Figure 1

31 pages, 6545 KB  
Article
Agent-Based Simulation Model for Rescuing Operations in Crowd Mass Disasters: Application to the Old City of Jerusalem
by Jawad Abusalama, Sazalinsyah Razali, Yun-Huoy Choo, Ali Attajer and Ismahen Zaid
Safety 2026, 12(2), 36; https://doi.org/10.3390/safety12020036 - 5 Mar 2026
Viewed by 340
Abstract
Crowd mass disasters occur over a relatively short time, and rescue operations in disasters, such as earthquakes, are challenging because of people’s behavior, type, or location. Therefore, it is essential to devise means and methods to manage such problems to minimize the consequences [...] Read more.
Crowd mass disasters occur over a relatively short time, and rescue operations in disasters, such as earthquakes, are challenging because of people’s behavior, type, or location. Therefore, it is essential to devise means and methods to manage such problems to minimize the consequences as much as possible. During disasters, rescue operations should be conducted in a timely conducted to save people’s lives. Otherwise, losses and consequences are severe, and if there are no proper rescuing operation models, the situation worsens, and the consequences are devastating. In particular, the allocation and coordination of limited rescue resources have a critical impact on response times and the number of lives saved. This paper aims to develop an Agent-Based Simulation (ABS) model for rescuing operations in crowd-mass disasters with six main intelligent agents. The proposed model explicitly represents the interactions among victims, rescuers, command-and-control entities, transportation assets, road networks, and affected infrastructure within a GIS-based urban environment. The developed model is based on an enhanced approach to improve rescue agents’ tasks allocation operations that enable modeling and simulation to make critical decisions for people to be rescued in a crowded mass disaster. Our task-allocation mechanism incorporates dynamic accessibility of roads, time-dependent rescue capacity, and context-aware prioritization of victims. Three related task-allocation strategies from the literature are used as baselines under identical scenarios, and performance is compared in terms of average rescue time and number of rescued victims. Results show that the proposed model achieves more efficient and robust rescue operations in most simulated experiments. Full article
Show Figures

Figure 1

18 pages, 339 KB  
Article
Entropy-Based Portfolio Optimization in Cryptocurrency Markets: A Unified Maximum Entropy Framework
by Silvia Dedu and Florentin Șerban
Entropy 2026, 28(3), 285; https://doi.org/10.3390/e28030285 - 2 Mar 2026
Viewed by 363
Abstract
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 [...] Read more.
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. Full article
17 pages, 1096 KB  
Article
Dynamic Risk Parity Portfolio Optimization: A Comparative Study with Markowitz and Static Risk Parity
by Peerapat Wattanasin, Thoedsak Chomtohsuwan and Tanpat Kraiwanit
J. Risk Financial Manag. 2026, 19(2), 135; https://doi.org/10.3390/jrfm19020135 - 11 Feb 2026
Viewed by 868
Abstract
Quantitative asset allocation remains a critical challenge in modern finance, particularly due to the inherent uncertainty of expected returns (μ) and the sensitivity of portfolio outcomes to the stability of portfolio weights. This study conducts a comparative empirical analysis of three portfolio strategies—MVO, [...] Read more.
Quantitative asset allocation remains a critical challenge in modern finance, particularly due to the inherent uncertainty of expected returns (μ) and the sensitivity of portfolio outcomes to the stability of portfolio weights. This study conducts a comparative empirical analysis of three portfolio strategies—MVO, Static RP, and Dynamic RP—using a long-only portfolio of eleven highly liquid assets, consisting of U.S. large-cap equities and gold, over the period 2015–2025. Results from historical backtesting indicate maintaining a competitive Sharpe ratio (1.418) and the lowest Maximum Drawdown (−0.2770) relative to Markowitz MVO (−0.3120) and Static RP (−0.2788). Although Markowitz delivers the numerically highest Sharpe ratio (1.655), this advantage is largely driven by in-sample optimization, with limited robustness under realistic implementation settings. In contrast, Dynamic RP demonstrates superior downside risk management, weight stability, and adaptability to changing market conditions, suggesting a more practical and resilient framework for real-world investment applications. Overall, the findings indicate that Dynamic Risk Parity provides an effective and robust alternative to traditional mean-variance optimization, offering investors a strategy that balances return potential, risk mitigation, and portfolio stability, while addressing key limitations of classical MVO approaches. Full article
(This article belongs to the Section Mathematics and Finance)
Show Figures

Figure 1

44 pages, 2282 KB  
Article
Particle Swarm Optimization with Stretching and Clustering for Asset Allocation
by Julien Chevallier
Int. J. Financial Stud. 2026, 14(2), 38; https://doi.org/10.3390/ijfs14020038 - 4 Feb 2026
Viewed by 475
Abstract
This paper develops a novel hybrid framework that integrates clustering-enhanced Particle Swarm Optimization (PSO) with stretching techniques to solve Markowitz’s quadratic portfolio optimization problem. The proposed approach avoids local optima traps that plague traditional optimization methods, while the stretching function modifications enhance the [...] Read more.
This paper develops a novel hybrid framework that integrates clustering-enhanced Particle Swarm Optimization (PSO) with stretching techniques to solve Markowitz’s quadratic portfolio optimization problem. The proposed approach avoids local optima traps that plague traditional optimization methods, while the stretching function modifications enhance the algorithm’s global search capabilities. The framework comprises four distinct algorithmic variants: a baseline SWARM PSO with stretching algorithm, and three clustering-enhanced extensions incorporating Hierarchical, K-means, and DBSCAN techniques. These clustering enhancements strategically group assets based on risk–return characteristics to improve portfolio diversification and risk management. Implementation in R enables comprehensive analysis of portfolio weight allocation patterns and diversification metrics across varying market structures. Empirical validation using daily price data from six major international stock market indices spanning January 2020 to December 2025 demonstrates the framework’s generalization capability in constructing buy-and-hold investment portfolios. The results reveal significant market-specific algorithmic effectiveness, with K-means variants achieving competitive efficacy in Eurostoxx and Belgian markets, DBSCAN demonstrating strong effectiveness in Chinese equity markets, Hierarchical clustering showing robust results in Indian market conditions, and the baseline SWARM algorithm exhibiting relative efficiency in French and Danish indices. Performance evaluation encompasses comprehensive risk-adjusted metrics, including Portfolio Return, Volatility, Sharpe Ratio, Calmar Ratio, and Value at Risk, providing portfolio managers with an adaptive, market-responsive optimization toolkit. Full article
Show Figures

Figure 1

26 pages, 2635 KB  
Article
Fuzzy Analytical Hierarchy Process-Based Multi-Criteria Decision Framework for Risk-Informed Maintenance Prioritization of Distribution Transformers
by Pannathon Rodkumnerd, Thunpisit Pothinun, Suwilai Phumpho, Neville Watson, Apirat Siritaratiwat, Watcharin Srirattanawichaikul and Sirote Khunkitti
Energies 2026, 19(2), 460; https://doi.org/10.3390/en19020460 - 17 Jan 2026
Viewed by 400
Abstract
Effective asset management is crucial for improving the reliability, resilience, and cost efficiency of distribution networks throughout the asset life cycle. Distribution transformers are among the most critical components, as their failures can cause extensive service interruptions and substantial economic impacts. Therefore, robust [...] Read more.
Effective asset management is crucial for improving the reliability, resilience, and cost efficiency of distribution networks throughout the asset life cycle. Distribution transformers are among the most critical components, as their failures can cause extensive service interruptions and substantial economic impacts. Therefore, robust and transparent maintenance prioritization strategies are essential, particularly for utilities managing several transformers. Traditional time-based maintenance, while simple to implement, often results in inefficient resource allocation. Condition-based maintenance provides a more effective alternative; however, its performance depends strongly on the reliability of indicator selection and weighting. This study proposes a systematic weighting framework for distribution transformer maintenance prioritization using a multi-criteria decision-making (MCDM) approach. Each transformer is evaluated across two dimensions, including health condition and operational impact, based on indicators identified from the literature and expert judgment. To address uncertainty and judgmental inconsistency, particularly when the consistency ratio (CR) exceeds the conventional threshold of 0.10, the Fuzzy Analytic Hierarchy Process (FAHP) is employed. Seven condition parameters characterize transformer health, while impact is quantified using five indicators reflecting failure consequences. The proposed framework offers a transparent, repeatable, and defensible decision-support tool, enabling utilities to prioritize maintenance actions, optimize resource allocation, and mitigate operational risks in distribution networks. Full article
(This article belongs to the Section F: Electrical Engineering)
Show Figures

Figure 1

31 pages, 707 KB  
Article
An Empirical Framework for Evaluating and Selecting Cryptocurrency Funds Using DEMATEL-ANP-VIKOR
by Mostafa Shabani, Sina Tavakoli, Hossein Ghanbari, Ronald Ravinesh Kumar and Peter Josef Stauvermann
J. Risk Financial Manag. 2026, 19(1), 29; https://doi.org/10.3390/jrfm19010029 - 2 Jan 2026
Viewed by 1393
Abstract
The acceleration of financial innovation and pro-crypto regulations in the digital asset space have spurred interest in cryptocurrencies among funds, and institutional and retail investors. Like any risky assets, investment in digital assets offers opportunities in terms of returns and challenges in terms [...] Read more.
The acceleration of financial innovation and pro-crypto regulations in the digital asset space have spurred interest in cryptocurrencies among funds, and institutional and retail investors. Like any risky assets, investment in digital assets offers opportunities in terms of returns and challenges in terms of risk. However, unlike traditional assets, digital assets like cryptocurrencies are highly volatile. Accordingly, applying conventional single-criterion financial metrics for portfolio construction may not be sufficient as the method falls short in capturing the complex, multidimensional risk-return dynamics of innovative financial assets like cryptocurrencies. To address this gap, this study introduces a novel, integrated hybrid Multi-Criteria Decision-Making (MCDM) framework that provides a structured, transparent, and robust approach to cryptocurrency fund selection. The framework seamlessly integrates three well-established operations research methodologies: the Decision-Making Trial and Evaluation Laboratory (DEMATEL), the Analytic Network Process (ANP), and the Vlse Kriterijumsk Optimizacija I Kompromisno Resenje (VIKOR) algorithm. DEMATEL is utilized to map and analyze the intricate causal interdependencies among a comprehensive set of evaluation criteria, categorizing them into foundational “cause” factors and resultant “effect” factors. This causal structure informs the ANP model, which computes precise criterion weights while accounting for complex feedback and dependency relationships. Subsequently, the VIKOR algorithm is invoked to use these weights to rank cryptocurrency fund alternatives, delivering a compromise between optimizing group utility and minimizing individual regret. To illustrate the application and efficacy of the proposed method, a diverse set of 20 cryptocurrency funds is analyzed. From the analysis, it is shown that foundational criteria, such as “Fee (%)” and “Annualized Standard Deviation,” are the primary causal drivers of financial performance outcomes of funds. This proposed framework supports strategic capital allocation in a rapidly evolving domains of digital finance. Full article
(This article belongs to the Section Financial Technology and Innovation)
Show Figures

Figure 1

28 pages, 2220 KB  
Article
Impact of Forest Ecological Compensation Policy on Farmers’ Livelihood: A Case Study of Wuyi Mountain National Park
by Chuyuan Pan, Hongbin Huang, Xiaoxia Sun and Shipeng Su
Forests 2026, 17(1), 53; https://doi.org/10.3390/f17010053 - 30 Dec 2025
Viewed by 353
Abstract
Forest ecological compensation policies (FECPs) are a key institutional arrangement for balancing ecological conservation and farmers’ development needs in national parks. Existing research has often treated such policies as a homogeneous whole, failing to clearly reveal the mechanisms through which different policy types [...] Read more.
Forest ecological compensation policies (FECPs) are a key institutional arrangement for balancing ecological conservation and farmers’ development needs in national parks. Existing research has often treated such policies as a homogeneous whole, failing to clearly reveal the mechanisms through which different policy types affect farmers’ livelihoods, while also paying insufficient attention to complex property-rights settings. This study takes Wuyi Mountain National Park—a typical representative of collective forest regions in southern China—as a case study. Based on 239 micro-survey datasets from farming households and employing the mprobit model and moderating effect models, it investigates the influence, mechanisms, and heterogeneity of farmers’ livelihood capital in terms of their livelihood strategy choices under the moderating roles of “blood-transfusion” and “blood-making” FECPs. The results show the following: (1) Among the sample farmers, livelihood strategies are distributed as follows: pure agricultural type (31.8%), out-migration for work type (20.5%), and commercial operation type (47.7%). (2) Farmers’ livelihood capital has a significant impact on their livelihood strategy choice, with different dimensions of capital playing distinct roles. (3) FECPs follow differentiated moderating pathways. “Blood-transfusion” policies emphasize compensation and buffering functions, reducing farmers’ livelihood transition pressure through direct cash transfers; “blood-making” policies reflect empowerment and restructuring characteristics, activating physical assets and reshaping the role of social capital through productive investment. Together, they constitute a complementary system of protective security and transformative empowerment. Accordingly, this study proposes policy insights such as building a targeted ecological compensation system that is categorized, dynamically linked, and precise; innovating compensation fund allocation mechanisms that integrate collective coordination with household-level benefits; optimizing policy design oriented toward enhancing productive capital; and establishing robust monitoring, evaluation, and adaptive management mechanisms for dynamic FECPs. Full article
(This article belongs to the Section Forest Economics, Policy, and Social Science)
Show Figures

Figure 1

31 pages, 443 KB  
Article
Asymptotic Formulas for the Haezendonck–Goovaerts Risk Measure of Sums with Consistently Varying Increments
by Jonas Šiaulys, Mantas Dirma, Neda Nakliuda and Luca Zanardelli
Axioms 2026, 15(1), 20; https://doi.org/10.3390/axioms15010020 - 26 Dec 2025
Viewed by 461
Abstract
The Haezendonck–Goovaerts (HG) risk measure defined on Orlicz spaces via the so-called normalised Young function is a direct generalisation of the Expected Shortfall risk measure. The HG measure is known to be a coherent one, thus making it more robust than some of [...] Read more.
The Haezendonck–Goovaerts (HG) risk measure defined on Orlicz spaces via the so-called normalised Young function is a direct generalisation of the Expected Shortfall risk measure. The HG measure is known to be a coherent one, thus making it more robust than some of the alternatives, such as Value-at-Risk, for aggregating and comparing risks, and at the same time more flexible for capital allocation problems, risk premium estimation, solvency assessment, and stress testing in insurance and finance. As random risk in practical applications is often assessed in a portfolio setting—a collection of insurance policies or financial assets, like stocks or bonds—we examine the situation in which the total portfolio risk is expressed as the sum of individual random risks. For this, we consider the sum Sn(ξ)=ξ1++ξn of possibly dependent and non-identically distributed real-valued random variables ξ1,,ξn with consistently varying distributions. Assuming that the collection {ξ1,,ξn} follows the dependence structure, similar to the asymptotic independence, we obtain the asymptotic estimations of the HG risk measure for the sum Sn(ξ) when the confidence level tends to 1. The formulas presented in our work show that in the case where a portfolio of random losses contains consistently varying losses and the others are asymptotically negligible, it is sufficient for risk assessment to consider only the tails of those dominant losses. Full article
(This article belongs to the Special Issue Numerical Analysis and Applied Mathematics)
Show Figures

Figure 1

27 pages, 710 KB  
Article
Robust Multi-Objective Optimization Model for Reserve and Credit Fund Allocation in Banking Under Conditional Value-at-Risk Constraints
by Moch Panji Agung Saputra, Diah Chaerani, Sukono and Mazlynda Md Yusuf
J. Risk Financial Manag. 2026, 19(1), 4; https://doi.org/10.3390/jrfm19010004 - 19 Dec 2025
Viewed by 597
Abstract
In the realm of financial management, optimizing the allocation of funds in banking companies is vital to their operational efficiency. Banks manage their funds by allocating them into reserve and credit funds as the main activities of banking. Optimizing these allocations ensures that [...] Read more.
In the realm of financial management, optimizing the allocation of funds in banking companies is vital to their operational efficiency. Banks manage their funds by allocating them into reserve and credit funds as the main activities of banking. Optimizing these allocations ensures that all assets are effectively utilized. However, real-life optimization problems often involve uncertainty, making deterministic data assumptions insufficient. Robust Optimization is a methodology that addresses these uncertainties by incorporating computational tools to solve optimization problems with uncertain data. The uncertainty approach used in robust optimization is polyhedral sets. In the context of banking, uncertainties influencing the allocation of reserve and credit funds include financial risks and returns. These risks can be quantified using Conditional Value-at-Risk (CVaR), a suitable measure for banking fund allocation due to its ability to accommodate varying risk characteristics under different business conditions. This study focuses on developing an optimization model for reserve and credit fund allocation in banking companies using a Multi-objective Robust CVaR approach with lexicographic, informed by business risk data and credit instruments. The resulting optimization model yields optimal allocations for reserve and credit funds, ensuring efficient asset utilization to support banking operations. This approach offers new perspectives for banks to achieve fund allocations that are not only regulatory compliant but also optimal. The implications of such optimal allocations include mitigating risks associated with reserve fund imbalances and enhancing profitability through optimal credit returns. Full article
(This article belongs to the Section Banking and Finance)
Show Figures

Figure 1

14 pages, 977 KB  
Article
Maximizing Portfolio Diversification via Weighted Shannon Entropy: Application to the Cryptocurrency Market
by Florentin Șerban and Silvia Dedu
Risks 2025, 13(12), 253; https://doi.org/10.3390/risks13120253 - 18 Dec 2025
Viewed by 1041
Abstract
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 [...] Read more.
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. Full article
Show Figures

Figure 1

11 pages, 2187 KB  
Article
Entropy and Minimax Risk Diversification: An Empirical and Simulation Study of Portfolio Optimization
by Hongyu Yang and Zijian Luo
Stats 2025, 8(4), 115; https://doi.org/10.3390/stats8040115 - 11 Dec 2025
Viewed by 708
Abstract
The optimal allocation of funds within a portfolio is a central research focus in finance. Conventional mean-variance models often concentrate a significant portion of funds in a limited number of high-risk assets. To promote diversification, Shannon Entropy is widely applied. This paper develops [...] Read more.
The optimal allocation of funds within a portfolio is a central research focus in finance. Conventional mean-variance models often concentrate a significant portion of funds in a limited number of high-risk assets. To promote diversification, Shannon Entropy is widely applied. This paper develops a portfolio optimization model that incorporates Shannon Entropy alongside a risk diversification principle aimed at minimizing the maximum individual asset risk. The study combines empirical analysis with numerical simulations. First, empirical data are used to assess the theoretical model’s effectiveness and practicality. Second, numerical simulations are conducted to analyze portfolio performance under extreme market scenarios. Specifically, the numerical results indicate that for fixed values of the risk balance coefficient and minimum expected return, the optimal portfolios and their return distributions are similar when the risk is measured by standard deviation, absolute deviation, or standard lower semi-deviation. This suggests that the model exhibits robustness to variations in the risk function, providing a relatively stable investment strategy. Full article
(This article belongs to the Special Issue Robust Statistics in Action II)
Show Figures

Figure 1

Back to TopTop