Portfolio Optimization

The growing adoption of artificial intelligence in financial services has transformed retirement planning and investment advisory processes. Machine learning models can analyze large volumes of financial and demographic data to generate personalized retirement product recommendations. However, many existing systems operate as black-box models, making it difficult for consumers and regulators to understand how recommendations are generated. This lack of transparency can reduce trust and create regulatory concerns. This paper proposes a framework for explainable retirement product recommendation that integrates risk-adjusted performance, cost efficiency, and income sufficiency metrics. The framework combines machine learning techniques with explainability tools to improve transparency and support informed financial decision-making. The proposed architecture includes data acquisition, evaluation, explainability, recommendation, and feedback components. The framework offers benefits for consumers, financial institutions, and regulators by improving trust, accountability, and retirement planning outcomes.

Style investing is one in which securities are classified based on some common characteristics in such a manner that assets in each group appear to be similar. When we discuss equity-based style investing, these styles may range from value and size to momentum and quality. Style investing can be defined as a rule based method of investing that generates unique long-term positive average returns across market and asset classes, with a low to zero correlation with o long-only asset classes. The present study is an attempt to examine the performance of the strategy of constructing single-style portfolios using Value and Momentum factors and also constructing a portfolio by combining Value and Momentum styles into a single portfolio using the bottom-up approach. In addition, the portfolios were rebalanced annually. Furthermore, the constructed portfolios were assessed on different risk and return parameters such as CAGR, max-drawdown, volatility, information ratio, tracking error and so on. The research indicates that integrating a specific style into a portfolio can enhance performance by yielding higher returns in exchange for the additional risk assumed. Moreover, it highlights that adopting a bottom-up approach to combining styles not only streamlines the process but also allows investors to gain exposure to multiple styles at once, thereby providing diversification benefits.

The paper shows that mean-CVaR-skewness portfolio optimization problems based on asymetric Laplace (AL) distributions can be transformed into quadratic optimization problems for which closed form solutions can be found. In this note, we show that such a result also holds for mean-risk-skewness portfolio optimization problems when the underlying distribution belongs to a larger class of normal mean-variance mixture (NMVM) models than the class of AL distributions. We then study the value at risk (VaR) and conditional value at risk (CVaR) risk measures of portfolios of returns with NMVM distributions. They have closed form expressions for portfolios of normal and more generally elliptically distributed returns, as discussed in and in . When the returns have general NMVM distributions, these risk measures do not give closed form expressions. In this note, we give approximate closed form expressions for the VaR and CVaR of portfolios of returns with NMVM distributions. Numerical tests show that our closed form formulas give accurate values for VaR and CVaR and shorten the computational time for portfolio optimization problems associated with VaR and CVaR considerably.

Gambling games provide a rich class of stochastic control problems. These include optimal betting, optimal stopping, and sequential decision-making under uncertainty, with objectives ranging from survival probability to asymptotic growth of wealth and risk-sensitive utility. This survey presents a self-contained treatment of dynamic programming techniques and solution methods in gambling stochastic processes, beginning with discrete-time controlled Markov systems and extending to continuous-time diffusions. We derive the Bellman equation from first principles, establish the principle of optimality, and prove standard convergence results for value and policy iteration. Classic models such as the Kelly criterion, gambler's ruin, and optimal stopping problems serve as concrete illustrations. We then develop continuous-time Hamilton-Jacobi-Bellman equations, risk-sensitive and constrained control, computational methods, and information-theoretic interpretations. The unifying theme is that gambling is best understood as a controlled stochastic process in which value functions encode optimal tradeoffs between reward, risk, and information.

High levels of correlation among fi nancial assets, as well as extreme losses, are typical during crisis periods. In such situations, quantitative asset allocation models are often not robust enough to deal with estimation errors and lead to identifying underperforming investment strategies. It is an open question if in such periods, it would be better to hold diversifi ed portfolios, such as the equally weighted, rather than investing in few selected assets. In this paper, we show that alternative strategies developed by constraining the level of diversifi cation of the portfolio, by means of a regularization constraint on the sparse l q -norm of portfolio weights, can better deal with the trade-off between risk diversifi cation and estimation error. In fact, the proposed approach automatically selects portfolios with a small number of active weights and low risk exposure. Insights on the diversifi cation relationships between the classical minimum variance portfolio, risk budgeting strategies, and diversifi cation-constrained portfolios are also provided. Finally, we show empirically that the diversifi cation-constrainedbased l q -strategy outperforms state-of-art methods during crises, with remarkable out-of-sample performance in risk minimization.

Quality Function Deployment (QFD) is widely used to translate customer needs into engineering targets. However, a key challenge in practice is prioritizing which engineering characteristics (ECs) to select and determining how to implement them under uncertainties in cost, risk, and technical data. This paper proposes a novel fuzzy goal programming (FGP) model that integrates the selection of ECs with the allocation of design alternatives (DAs). The model seeks to maximize customer satisfaction (CS) while minimizing cost and technical risk, using fuzzy set theory to capture imprecision in development data. The approach is demonstrated through an electric vehicle powertrain case study, which shows the generation of robust Pareto-optimal solutions. The results indicate that the model offers managers a practical and quantitative decision tool for strategic product design under uncertain conditions.

The Portfolio Optimization task has long been studied in the Financial Services literature as a procedure to identify the basket of assets that satisfy desired conditions on the expected return and the associated risk. A wellknown approach to tackle this task is the maximization of the Sharpe Ratio, achievable with a problem reformulation as Quadratic Programming. While the sole Sharpe Ratio could be efficiently optimized via classical solvers, in business scenarios it is common that multiple additional needs arise, which have to be integrated in the optimization model as either new constraints or objective function terms. Then, in general, the problem may become nonconvex and hence could potentially be not efficiently solvable via classical techniques anymore. One example of such additional objective function term consists of maximizing a diversification measure penalizing portfolios holding significant portions of investments on assets belonging to the same sector, while favouring solutions that diversify over multiple sectors. The problem of optimizing both the Sharpe Ratio and a diversification term can be mapped to a QUBO and be solved via quantum annealing devices or Hybrid Computing approaches, which are expected to find high quality solutions. We propose a new QUBO formulation for the task described and provide the mathematical details and required assumptions, showing the ease of modeling the optimization as QUBO against the effort that would be required by classical strategies. We derive results via the available QUBO solvers, as well as discussing the behaviour of Hybrid approaches to tackle large scale problems in the near term. We finally elaborate on the results showing the trade-off between the observed values of the portfolio's Sharpe Ratio and diversification, as a natural consequence of solving a multi-objective optimization problem.

The Portfolio Optimization task has long been studied in the Financial Services literature as a procedure to identify the basket of assets that satisfy desired conditions on the expected return and the associated risk. A wellknown approach to tackle this task is the maximization of the Sharpe Ratio, achievable with a problem reformulation as Quadratic Programming. While the sole Sharpe Ratio could be efficiently optimized via classical solvers, in business scenarios it is common that multiple additional needs arise, which have to be integrated in the optimization model as either new constraints or objective function terms. Then, in general, the problem may become nonconvex and hence could potentially be not efficiently solvable via classical techniques anymore. One example of such additional objective function term consists of maximizing a diversification measure penalizing portfolios holding significant portions of investments on assets belonging to the same sector, while favouring solutions that diversify over multiple sectors. The problem of optimizing both the Sharpe Ratio and a diversification term can be mapped to a QUBO and be solved via quantum annealing devices or Hybrid Computing approaches, which are expected to find high quality solutions. We propose a new QUBO formulation for the task described and provide the mathematical details and required assumptions, showing the ease of modeling the optimization as QUBO against the effort that would be required by classical strategies. We derive results via the available QUBO solvers, as well as discussing the behaviour of Hybrid approaches to tackle large scale problems in the near term. We finally elaborate on the results showing the trade-off between the observed values of the portfolio's Sharpe Ratio and diversification, as a natural consequence of solving a multi-objective optimization problem.

the correlation between the returns of PT Bank Mandiri Tbk. (BMRI) and PT Indofood Sukses Makmur Tbk. (INDF) using relative beta analysis as a foundation for portfolio diversification strategy. Monthly closing price data from both stocks were used to compute monthly returns over a twelve-month period. A simple linear regression approach was applied to calculate the relative beta, which quantifies the return sensitivity of one stock relative to the other. The result shows a relative beta of 0.1220, indicating a very low degree of co-movement between the two stocks' returns. This low correlation implies significant diversification benefits when the two stocks are combined in a single portfolio. The findings are consistent with modern portfolio theory, confirming that assets with low return correlation can reduce overall portfolio risk without proportionally sacrificing return potential. Penelitian ini mengkaji keterkaitan antara return saham PT Bank Mandiri Tbk. (BMRI) dan PT Indofood Sukses Makmur Tbk. (INDF) melalui pendekatan analisis beta relatif sebagai landasan perumusan strategi diversifikasi portofolio. Data yang digunakan berupa harga penutupan bulanan kedua saham selama dua belas bulan, mulai Januari hingga Desember, yang kemudian diolah menjadi return bulanan. Dengan menerapkan regresi linier sederhana, nilai beta relatif dihitung untuk mengukur sensitivitas return BMRI terhadap pergerakan return INDF atau sebaliknya sehingga mencerminkan hubungan kovariasi di antara keduanya. Hasil analisis menunjukkan bahwa beta relatif BMRI terhadap INDF sebesar 0,1220, yang mengindikasikan tingkat sensitivitas yang sangat rendah. Artinya, pergerakan return INDF hanya mampu menjelaskan sebagian kecil variasi return BMRI. Rendahnya korelasi ini secara teoritis memberikan manfaat diversifikasi yang signifikan apabila kedua saham dikombinasikan dalam satu portofolio. Temuan ini sejalan dengan prinsip dasar teori portofolio modern, bahwa penggabungan aset dengan korelasi rendah dapat menekan risiko total portofolio tanpa harus mengorbankan potensi imbal hasil secara proporsional. Penelitian ini diharapkan memberikan kontribusi bagi investor individu maupun manajer investasi dalam mengoptimalkan alokasi aset di pasar modal Indonesia.

The Indian share market has experienced substantial growth during 2025-2026 due to increased retail participation, digital trading infrastructure, foreign institutional investments, and rapid expansion in technology-driven industries. Portfolio optimization in such a volatile and diversified market environment requires mathematically rigorous models capable of incorporating realistic trading restrictions and sectoral dynamics. This study develops a mixed-integer linear programming (MILP) framework for portfolio optimization using current data from the National Stock Exchange (NSE) of India. Unlike traditional continuous portfolio models, the proposed framework incorporates practical financial constraints including integer share purchases, transaction costs, sectoral diversification, budget limitations, and exposure control across multiple industries. The analysis considers major Indian blue-chip companies from diversified sectors including information technology, banking, energy, automobile, pharmaceuticals, telecommunications, and infrastructure. Current market data from Reliance Industries, Tata Consultancy Services (TCS), Infosys, HDFC Bank, ICICI Bank, Larsen & Toubro, Sun Pharma, Bharti Airtel, and Tata Motors are utilized for comparative analysis. 1 Computational results demonstrate that the MILP approach generates practically implementable portfolios while maintaining balanced sectoral exposure and controlled investment risk. The results further reveal that the information technology and banking sectors continue to dominate expected returns during 2025-2026, whereas energy and pharmaceutical sectors provide portfolio stability under market uncertainty.

Critical infrastructure environments depend on communication systems whose performance must be assessed not only by functional delivery, but by their capacity to preserve continuity, traceability, maintainability, and operational trust under changing technical conditions. In such contexts, voice and data networks support coordination, supervision, incident response, maintenance logistics, and the stable exchange of operational information across distributed environments. Consequently, architectural decisions related to redundancy, failover, segmentation, technical documentation, validation procedures, and secure configuration baselines directly affect resilience and long-term service reliability. This article develops an applied technical analysis of voice and data network architecture for critical infrastructure, emphasizing that architecture in such environments must be treated as a lifecycle engineering discipline rather than a set of isolated installation tasks. The study adopts a qualitative and practice-informed methodology grounded in systems security engineering, operational technology security guidance, redundancy logic, and configuration management principles. The discussion demonstrates that resilient communication architectures require the coordinated integration of five dimensions: continuity planning, configuration discipline, documentation traceability, validation routines, and security-by-design. The article's original contribution lies in presenting an integrated framework that connects these dimensions into a unified model for architecture, deployment, and operational sustainment in critical infrastructure environments. Rather than proposing a new protocol or device-specific solution, the study advances a field-oriented architecture perspective capable of supporting more reliable, maintainable, and defensible communication systems in environments where failure has amplified operational consequences.

Exchange rate fluctuations are critical in ensuring economic stability and shaping foreign investment, while foreign currencies serve as asset and wealth diversification instruments. This study aims to predict foreign exchange rates with a multidimensional geometric Brownian motion model and determine the optimal portfolio fund allocation with the Markowitz model using the Moore-Pendrose method. The multidimensional GBM model was employed for its ability to capture the volatility and interdependence among multiple currencies, making it more suitable for multi-asset portfolios than univariate models. The Markowitz model was used to determine the optimal asset allocation that achieves a specified expected return with minimal risk, while the Moore-Penrose method was applied to address matrix inversion challenges in high-dimensional data. Using data from 2023 to April 2024 on the Indonesian rupiah against the Singapore Dollar (SGD), Chinese Yuan (CNY), and Euro (EUR), this study finds that the multidimensional GBM model effectively forecasts exchange rate movements, as indicated by MAPE values below 10% for each currency. "The optimal portfolio yields a risk of 0.28% and an expected return of 0.009%, with asset allocations of 90.3% in SGD, 8.2% in CNY, and 1.5% in EUR. The dominance of SGD in the optimal portfolio suggests it was the most favorable investment option against the rupiah during the study period. This reflects Singapore's strong economic fundamentals and strategic position as a global financial hub. These findings provide valuable insights for investors and financial analysts seeking to manage currency risk and enhance returns through data-driven diversification strategies.

Introdction The breadth and lack of general consensus on the definition of systemic risk have led to a variety of measurement methods and metrics for this type of risk. A large number of different metrics have emerged, presenting new patterns that had not been considered before the 2008 financial crisis. Although each of the definitions presented for systemic risk has led to the introduction and improvement of systemic-risk measures, this proliferation makes it difficult to choose a comprehensive, superior measure. The importance of studying systemic risk became even more evident after the 2008 crisis. What distinguishes this study from others is that it attempts to introduce a superior measure by comparing the performance of the candidate measures. The tools examined include systemic-risk measures based on return correlations, which are very simple to apply in the context of financial turbulence.

In recent years, cryptocurrency has been widely adopted and seen as an alternative investment tool for investors. However, which cryptocurrency to invest in and how much to invest becomes a problem. Since there is a conflict of multiple criteria, portfolio optimization (PO) is needed to solve the problem. In this study, an Artificial Bee Colony (ABC) algorithm has been developed based on Markowitz's mean-variance model (M-MVM). With this method, the portfolio of cryptocurrencies has been tried to be optimized. Hourly data of 12 cryptocurrencies between 01.09.2020 and 01.04.2021 were used as data. It has been observed that the ABC algorithm achieves good results in the solution of the problem in a reasonable time. In addition, the method was tested with different parameter values and different risk-averse coefficient values (λ).

A measure for portfolio risk management is proposed by extending the Markowitz mean-variance approach to include the left-hand tail effects of asset returns. Two risk dimensions are captured: asset covariance risk along risk in left-hand tail similarity and volatility. The key ingredient is an informative set on the left-hand tail distributions of asset returns obtained by an adaptive clustering procedure. This set allows a left tail similarity and left tail volatility to be defined, thereby providing a definition for the left-tail-covariance-like matrix. The convex combination of the two covariance matrices generates a “two-dimensional” risk that, when applied to portfolio selection, provides a measure of its systemic vulnerability due to the asset centrality. This is done by simply associating a suitable node-weighted network with the portfolio. Higher values of this risk indicate an asset allocation suffering from too much exposure to volatile assets whose return dynamics behave ...

A measure for portfolio risk management is proposed by extending the Markowitz mean-variance approach to include the left-hand tail effects of asset returns. Two risk dimensions are captured: asset covariance risk along risk in left-hand tail similarity and volatility. The key ingredient is an informative set on the left-hand tail distributions of asset returns obtained by an adaptive clustering procedure. This set allows a left tail similarity and left tail volatility to be defined, thereby providing a definition for the left-tail-covariance-like matrix. The convex combination of the two covariance matrices generates a “two-dimensional” risk that, when applied to portfolio selection, provides a measure of its systemic vulnerability due to the asset centrality. This is done by simply associating a suitable node-weighted network with the portfolio. Higher values of this risk indicate an asset allocation suffering from too much exposure to volatile assets whose return dynamics behave ...

Background. Human activities are exerting increasing pressure on the ocean, threatening marine biodiversity and the many benefits it provides to people. Allocating adequate space to enable the sustainable and equitable use of the ocean resources, while ensuring cost-effective conservation and restoration of marine ecosystems is particularly challenging in light of ambitious global, regional, and national commitments, such as those established by the Global Biodiversity Framework. In this context, Systematic Conservation Planning (SCP) offers a robust framework to prioritize conservation actions that safeguard biodiversity while minimizing costs and facilitating dialogue among maritime sectors.

Methodology. The scoping review here assesses the challenges in SCP implementation and the obstacles preventing its adoption in guiding decision-making for the achievement of conservation objectives in harmony with human uses of marine resources. The 149 studies analysed, spanning from 2002 to early 2023, are distributed across all continents and encompass nine biogeographic realms.

Results. Our analysis shows that only a limited number of SCP-based spatial plans have been implemented and just one study explicitly demonstrated the attainment of conservation targets defined through the SCP process. Inadequate criteria for assessing plan effectiveness and weak linkages between academic research and management practice were identified as significant impediments to the effective implementation of SCP outcomes.

Conclusions. The review synthetizes context-specific recommendations, emphasizing that good practices vary across countries according to their geopolitical and economic settings, from small island developing states to middle- and high-income countries. Our study highlights that aligning SCP objectives with international policy frameworks is essential for addressing gaps in conservation and restoration planning and for embedding SCP within global governance processes.

Prednáška je venovaná finančnému investovaniu. Z tejto oblasti som v roku 1998 vypracoval diplomovú prácu na tému Softvérová podpora modelovania očakávaného výnosu a rizika portfólia. Súčasťou diplomovej práce bol aj program IDPORT realizovaný v protredí Excelu 7.0 Program umožňoval zobraziť aproximáciu hranice množiny investičných príležitostí v priestore očakávaného výnosu a rizika portfólia pri povolených alebo zakázaných krátkych predajoch. Každý bod hranice množiny investičných príležitostí

The Indian stock market has seen a lot of growth in the past ten years. This is because more people are investing in the market and there are systems in place for trading. The government has also made some changes to help the market. All these things have made the market bigger. It is also more complicated for people to decide where to invest their money. This study looks at how four important parts of the stock market did over ten years. These parts are Banking, Information Technology, Pharmaceuticals and Moving Consumer Goods. The study uses data from twenty companies, five from each part to see how they did from January 2015 to December 2025. This study uses tools to see how each part of the market did. It looks at how much money the companies made, how much risk they took and how well they did compared to how much risk they took. The study also looks at how the companies did during some events like when the government took away some currency in 2016, the COVID-19 pandemic in 2020 and the trade problems with the US in 2024 and 2025. What the study found out is that the Moving Consumer Goods part of the market did the best. It generated the highest return compared to how much risk it took. The Banking part of the market made a lot of money. It was also very risky. The Information Technology and Pharmaceuticals parts of the market did not do well especially during the trade problems with the US in 2025. The study is important because it can help people make decisions about where to invest their money. It can also help the government make decisions about how to regulate the market. The Indian stock market is a part of the Indian economy and the Indian stock market has many different parts, like Banking, Information Technology, Pharmaceuticals and Fast-Moving Consumer Goods and each part of the Indian stock market has its own strengths and weaknesses.

Governance, ESG Environmental, and ESG Social and Energy Consumption were significant predictors of ESG performance. In this work, a machine learning model is introduced to forecast company Environmental, Social and Corporate Governance (ESG) performance as part of a sustainable business strategy. We used a simulated dataset created around 1,000 companies, in nine industries and seven regions (period 2015-2025) for monitoring model development. Three models were applied: a Dummy Regressor baseline, the XGBoost with Improved Hunter-Prey Optimization (IHPO) and the Grey Wolf Optimization (GWO) tuned model Random Forest. The IHPO-XGBoost performed the best, with an R² of 0.9982 and RMSE of 0.6479. Significant predictors of ESG performance were ESG Governance, ESG Environmental AND ESG Social and Energy Consumption. This results demonstrate the benefits of bio-inspired optimization for improved predictive accuracy, and provide valuable implications for managers intending to infuse ESG considerations in business strategy.

Este trabajo reconstruye un desplazamiento histórico y, a la vez, un cambio en las formas de gobierno económico que afecta tanto a la empresa como a la experiencia ordinaria del trabajo. El hilo conductor es doble. Por un lado, se examina cómo la corporación deja de legitimarse principalmente por su continuidad productiva y pasa a organizarse en torno a la validación bursátil, con temporalidades cada vez más cortas y con una disciplina que opera a través del precio. Por otro lado, se muestra cómo esa disciplina se vuelve operativa y exportable cuando se apoya en dispositivos de medición y verificación continua, capaces de distribuir responsabilidades y riesgos hacia individuos que deben adaptarse a señales cambiantes. En ese marco, se busca describir un mecanismo de articulación entre criterios de evaluación, dispositivos técnicos de control y subjetividades que aprenden a vivir bajo comparación permanente. La pregunta que guía el recorrido es cómo una lógica que nace y se consolida en el mundo corporativo y financiero termina reorganizando otras esferas de la vida, produciendo aislamiento, competencia cotidiana y una sensación ambigua de libertad que convive con nuevas formas de dependencia. La primera parte ordena cronológicamente el pasaje desde la empresa organizada en torno a la reinversión productiva, propia de la posguerra, hacia la primacía accionaria.

The solvability of dynamic decision problems suffer from the curse of dimensionality which limits the planning horizon one can afford for mapping the real problem into a numeric solvable dynamic optimization model. In this note, stochastic multistage programming is applied to dynamic fixed-income portfolio selection. We report on the goodness fixed income portfolio problems are currently solved with, using barycentric approximation. In particular, it is illustrated how the planning horizon becomes effective with respect to the numerical effort for solving the programs. The computational results serve as benchmark for decomposition methods of mathematical programming.

Purpose: This study provides a comprehensive analysis of the evolution of portfolio optimization over the last three decades, employing systematic review and advanced bibliometric techniques to map key trends, influential works, and significant contributors in the field. Design/Methodology/Approach: Adhering to PRISMA guidelines, we conducted a systematic review and bibliometric analysis of 1,000 articles sourced from the Web of Science database, spanning from 1989 to 2023. Advanced bibliometric tools, including citation analysis, co-occurrence analysis, and network visualization, were utilized to identify prominent authors, influential journals, and emerging research themes. Findings: Our analysis reveals a significant growth in portfolio optimization literature, particularly in recent years. Key findings include the identification of pivotal authors, foundational papers, and leading journals that have shaped the field. The study also traces the methodological evolution from traditional models, like Markowitz's Modern Portfolio Theory, to contemporary approaches incorporating artificial intelligence and machine learning. Practical Implications: This study offers valuable insights for researchers and practitioners by highlighting critical developments in portfolio optimization. It also suggests areas for future research, particularly in integrating advanced data analytics and AI-driven methodologies into portfolio management. Originality/Value: This paper stands out by combining systematic review with a comprehensive bibliometric analysis, offering a holistic view of the portfolio optimization landscape. It not only synthesizes past research but also identifies emerging trends and gaps, providing a foundation for future explorations in this dynamic field.

Finding the best investment strategies has been a never-ending challenge for investors and financial professionals in the constantly changing financial market environment. The idea of financial portfolio optimization, a complex procedure that aims to navigate the complex trade-off between risk and return, is at the heart of this endeavour. While fundamental, traditional approaches to portfolio optimization frequently need to capture the complexity present in today's dynamic markets. This paper aims to provide a comprehensive literature review on portfolio optimisation of novel approaches, analysing their key features, advantages, and limitations. From the supplementary materials, Research Articles and Book chapters.

We study the optimal power flow problem with switching (or, equivalently, the line expansion problem) under demand uncertainty. Specifically, we consider the line-use variables at the first stage and the currentor power-flow at the second stage of two affinely adjustably robust formulations.

We study the optimal power flow problem with switching (or, equivalently, the line expansion problem) under demand uncertainty. Specifically, we consider the line-use variables at the first stage and the current- or power-flow at the second stage of two affinely adjustably robust formulations.

The liability stream of insurance companies often stretches several years into the future. Therefore, there is always the need to determine a portfolio of bonds or other assets whose cash-flows replicate those of the liability stream. Insurance regulatory authorities require that insurance companies must demonstrate solvency. To achieve this, an insurance company needs to determine a fair market value of its liability by finding a replicating portfolio consisting of default-free bonds. This paper presents a class of optimization models that could be employed for portfolio optimization in the presence of background risk.

Project portfolio selection is a common problem in modern organizations. The allocation of resources to projects taking into account (a) the multi-criteria evaluation of projects and (b) the policy requirements for the final portfolio, is often addressed with a combination of multi-criteria analysis for the evaluation part and integer programming for the optimization part. However, the final portfolio is sensitive to changes in the importance of criteria, due to the multi-criteria evaluation of the projects which is the driver of the optimization. In the proposed approach, we take into account the inherent subjectivity expressed in the weights of criteria using a variation of the Iterative Trichotomic Approach method (Mavrotas and Pechak in Int J Mult Criteria Decis Mak 3:79-97, 2013). Specifically, we use an iterative process that starts considering portfolios that emerge from optimizing separately each criterion and gradually converging to the original set of criteria weights. The additional information provided to the decision maker by the proposed method, is that she/ he can realize if the selection or exclusion of a specific project in the final portfolio is objective or it depends on the subjective weights and to what extent, while the conventional MCDA-IP approach does not differentiate the selected projects according to the imposed degree of subjectivity. The method is illustrated with a real data application from a project portfolio selection problem in Greece with 540 R&D projects that have to follow sectoral and geographical constraints.

Robotic financial advisors (robo-advisors) have emerged as a purported low-cost and low-hassle alternative to traditional investment advisers and broker-dealers. This type of advisor assists financial institutions in employing asset-allocation models and algorithms to invest client portfolios, typically in exchange-traded funds. In this paper, we focus on reviewing the current state of the art in the provision of financial advice and discuss how regulatory agencies have interacted with aspects of robo-advising.

The Black-Scholes framework assumes constant volatility and continuous diffusion, yet empirical markets exhibit volatility smiles, jumps, and strong feedback effects driven by trading activity. This paper develops a geometric extension in which implied volatility defines a Riemannian metric over the strike-maturity space. We further incorporate jump processes, dealer gamma feedback, and market microstructure variables including liquidity, order flow, and inventory. The resulting framework models financial markets as evolving on a state-dependent curved manifold, where geometry is endogenously shaped by trading activity. This provides a unified interpretation of volatility structure, regime shifts, and nonlinear price formation across micro and macro scales.

Resumen. El trabajo introduce el concepto de riesgo en la teoría financiera, destacando su distinción respecto de la incertidumbre, según lo planteado por Frank H. Knight. Mientras que el riesgo puede ser cuantificado mediante distribuciones de probabilidad, la incertidumbre se caracteriza por la imposibilidad de realizar dicha estimación. En el análisis financiero, el riesgo se asocia principalmente con la volatilidad de los rendimientos, siendo el desvío estándar una de sus medidas más utilizadas. El artículo revisa los principales marcos teóricos, entre ellos la hipótesis de eficiencia de los mercados y el Modelo de Valoración de Activos Financieros (CAPM), desarrollado por William F. Sharpe, que permite descomponer el riesgo en sus componentes sistemático y no sistemático. Asimismo, se analiza el papel de la diversificación en la reducción del riesgo específico. Finalmente, se examinan las limitaciones de los modelos tradicionales de medición del riesgo, en particular su dependencia de datos históricos y de supuestos como la normalidad y la eficiencia de los mercados. Se concluye que la medición del riesgo es inherentemente imperfecta y requiere una interpretación cuidadosa en su aplicación práctica.

In this paper we consider an MPC algorithm for portfolio optimization type problems. We provide explicit expressions of the cost of MPC trajectories in dependence of the optimization horizon, the sampling time and the predictor. The asymptotic analysis for the cost is developed.

The increasing need for real-time data processing in modern digital ecosystems
has driven the adoption of event-driven architectures and streaming platforms.
This paper proposes a unified log-centric architecture for real-time systems
using event-driven streaming pipelines powered by Apache Kafka. By
positioning Kafka’s distributed commit log as the central data backbone, the
architecture enables seamless integration of data producers and consumers
while ensuring high throughput, low latency, and fault tolerance. The
approach emphasizes decoupled microservices, durable event storage, and
replayable data streams, facilitating scalability and system resilience. Key
design patterns such as event sourcing, stream processing, and stateful
aggregations are explored to enhance data consistency and processing
efficiency. Additionally, the architecture incorporates mechanisms for failure
handling, exactly-once processing semantics, and real-time analytics. The
proposed model demonstrates significant improvements in system reliability,
operational flexibility, and responsiveness, making it well-suited for highdemand domains such as finance, e-commerce, and IoT-driven applications

The major aim of Investors and Asset managers of companies is to make better returns at a given predictable return at near risk. In depth study of portfolio administration is performed in accordance with the portfolio examination formed by six freely recorded companies in India. The paper is an endeavour, an event that is productive broadening amid a difficult time working out the Markowitz show. Others, solutions for present portfolio hazard administration for the Indian monetary showcase are discussed. The inquiry about technique centres on applying an advanced portfolio hypothesis, with fundamental accentuation on the Markowitz productive wilderness, hazards, return and portfolio optimization. The information is basically based on the best performing divisions of the Indian economy, and six companies are chosen from each segment to test for enhancement. Key discoveries are that there is a greater chance of being lower than the weighted hazard of the stocks. Therefore, productive expansion is accomplished.

We apply the path signature transform-a canonical lossless encoding of multidimensional time series rooted in Chen's theorem (1954) and Rough Path Theory (Lyons 1998)-to the joint trajectory of bid price, ask price, bid volume, and ask volume extracted from limit order book (LOB) data. Truncating the signature at order 4 yields a 341-dimensional feature vector that constitutes a sufficient statistic for predicting the next mid-price direction without any manual feature engineering. Evaluated on the FI-2010 benchmark dataset (NASDAQ, 10 stocks, 10 trading days, 10-level LOB) and on proprietary US equity tick data (2020-2024), the signature feature set outperforms standard hand-crafted LOB features (OBI, spread, VPIN, microprice) by 35-56% in terms of Information Coefficient (IC) at 100-500ms prediction horizons. We further demonstrate that the 5 most informative signature terms-cross-variation of bid price and bid volume, Lévy area between bid and ask price paths, and three third-order interaction terms-have direct microstructure interpretations, suggesting that the signature is not merely a black-box feature extractor but a structured decomposition of LOB information. GPUaccelerated computation via the Signatory library achieves full 341-feature extraction in under 0.8ms, making the approach compatible with live HFT deployment.

Abstract:
Background: The integration of the Artificial Intelligence (AI) within the scientific
computing as well as engineering systems has mainly had gained substantial traction due
to its actual ability to improve computational efficiency, precision, and the decision-
making. Some of the algorithms that are considered as AI include machine learning, deep
learning and evolutionary algorithm and that it can also be utilized to transform the rock
in numerous areas of science and engineering.
Methods: AI techniques are mainly being employed within the scientific computing for
the context of data analysis, simulation, and also to mainly identify the various patterns.
It finds application mainly as neural networks to predict very complex systems, genetic
algorithms to optimization in engineering design and adaptive systems through the use of
reinforcement learning. Besides that, AI is also used in physics, chemistry and biology
and resolves issues related to life in the curb using devices, including the support vectors
machines and fuzzy logic.
Results: It has been proved that the AI could be easily used in optimization of the
engineering systems designs, increase reliability of the engineering systems and provide
predictive maintenance solution within the engineering systems. An example; the flight
control systems have been upgraded with the help of an AI-based model where in the
field of mechanical engineering system, AI is applied in an attempt to optimize the
material usage and reduce the number of used consumed energy. The positive
breakthroughs in the sphere of climate and drug development as well as material science
were also the results of scientific simulations with the assistance of AI provided.
Discussion: The issues that are surrounding the use of AI still remain even following the
incredible improvement. These entail tremendous and well-trained data needed,
computing equipment, not to mention, artificial intelligence and singular-engineering
performance. Nevertheless, this issue can be resolved since the unceasing search and
development of AI algorithms and computer power will endeavor to enhance
performance and reduce grade by cutting the cost down the line.
Conclusion: The scientific Computer systems and engineering applications have been
experienceing a gradual increase and have revolutionized the scientific field of
automation, optimization, and predictive analysis. The future of including AI to the field is
independently shutting the prospect of blindness to accelerate the efficaces, application
in the world and the existence of unficing the world of the incurable issues that will
additional energize further research and technological rise in the future.

We study portfolio optimization problems where the drift rate of the stock is Markov-modulated and the driving factors cannot be observed by the investor. Using results from filter theory we reduce this problem to one with complete observation. In the case of logarithmic and power utility we solve the problem explicitly with the help of stochastic control methods. It turns out that the value function is a classical solution of the corresponding Hamilton-Jacobi-Bellman equation. As a special case we investigate the so-called Bayesian case, i.e. the drift rate is unknown but does not change during time. In this case we prove a number of interesting properties of the optimal portfolio strategy. In particular, using the likelihood-ratio ordering, we can compare the optimal investment in the case of observable drift rate to the one in the case of unobservable drift rate. Thus, we also obtain the sign of the drift risk.

A financial market with one bond and one stock is considered where the risk free interest rate, the appreciation rate of the stock and the volatility of the stock depend on an external finite state Markov chain. We investigate the problem of maximizing the expected utility from terminal wealth and solve it by stochastic control methods for different utility functions. Due to explicit solutions it is possible to compare the value function of the problem to one where we have constant (average) market data. The case of benchmark optimization is also considered.

We study portfolio optimization problems in which the drift rate of the stock is Markov modulated and the driving factors cannot be observed by the investor. Using results from filter theory, we reduce this problem to one with complete observation. In the cases of logarithmic and power utility, we solve the problem explicitly with the help of stochastic control methods. It turns out that the value function is a classical solution of the corresponding Hamilton-Jacobi-Bellman equation. As a special case, we investigate the so-called Bayesian case, i.e. where the drift rate is unknown but does not change over time. In this case, we prove a number of interesting properties of the optimal portfolio strategy. In particular, using the likelihood-ratio ordering, we can compare the optimal investment in the case of observable drift rate to that in the case of unobservable drift rate. Thus, we also obtain the sign of the drift risk.

We consider an insurance company whose risk reserve is given by a Brownian motion with drift and which is able to invest the money into a Black–Scholes financial market. As optimization criteria, we treat mean-variance problems, problems with other risk measures, exponential utility and the probability of ruin. Following recent research, we assume that investment strategies have to be deterministic. This leads to deterministic control problems, which are quite easy to solve. Moreover, it turns out that there are some interesting links between the optimal investment strategies of these problems. Finally, we also show that this approach works in the Levy process framework.

A financial market with one bond and one stock is considered where the risk free interest rate, the appreciation rate of the stock and the volatility of the stock depend on an external finite state Markov chain. We investigate the problem of maximizing the expected utility from terminal wealth and solve it by stochastic control methods for different utility functions. Due to explicit solutions it is possible to compare the value function of the problem to one where we have constant (average) market data. The case of benchmark optimization is also considered.

We consider a financial market with one bond and one stock. The dynamics of the stock price process allow jumps which occur according to a Markov‐modulated Poisson process. We assume that there is an investor who is only able to observe the stock price process and not the driving Markov chain. The investor's aim is to maximize the expected utility of terminal wealth. Using a classical result from filter theory it is possible to reduce this problem with partial observation to one with complete observation. With the help of a generalized Hamilton–Jacobi–Bellman equation where we replace the derivative by Clarke's generalized gradient, we identify an optimal portfolio strategy. Finally, we discuss some special cases of this model and prove several properties of the optimal portfolio strategy. In particular, we derive bounds and discuss the influence of uncertainty on the optimal portfolio strategy.

We consider stochastic control problems with jump-diffusion processes and formulate an algorithm which produces, starting from a given admissible control π, a new control with a better value. If no improvement is possible, then π is optimal. Such an algorithm is well-known for discrete-time Markov Decision Problems under the name Howard’s policy improvement algorithm. The idea can be traced back to Bellman. Here we show with the help of martingale techniques that such an algorithm can also be formulated for stochastic control problems with jump-diffusion processes. As an application we derive some interesting results in financial portfolio optimization.

We study portfolio optimization problems in which the drift rate of the stock is Markov modulated and the driving factors cannot be observed by the investor. Using results from filter theory, we reduce this problem to one with complete observation. In the cases of logarithmic and power utility, we solve the problem explicitly with the help of stochastic control methods. It turns out that the value function is a classical solution of the corresponding Hamilton-Jacobi-Bellman equation. As a special case, we investigate the so-called Bayesian case, i.e. where the drift rate is unknown but does not change over time. In this case, we prove a number of interesting properties of the optimal portfolio strategy. In particular, using the likelihood-ratio ordering, we can compare the optimal investment in the case of observable drift rate to that in the case of unobservable drift rate. Thus, we also obtain the sign of the drift risk.

We consider an investment problem where observing and trading are only possible at random times. In addition, we introduce drawdown constraints which require that the investor's wealth does not fall under a prior fixed percentage of its running maximum. The financial market consists of a riskless bond and a stock which is driven by a Lévy process. Moreover, a general utility function is assumed. In this setting we solve the investment problem using a related limsup Markov decision process. We show that the value function can be characterized as the unique fixed point of the Bellman equation and verify the existence of an optimal stationary policy. Under some mild assumptions the value function can be approximated by the value function of a contracting Markov decision process. We are able to use Howard's policy improvement algorithm for computing the value function as well as an optimal policy. These results are illustrated in a numerical example.

We investigate the problem of minimizing a certainty equivalent of the total or discounted cost over a finite and an infinite horizon which is generated by a Markov Decision Process (MDP). The certainty equivalent is defined by U -1 (E U (Y )) where U is an increasing function. In contrast to a risk-neutral decision maker this optimization criterion takes the variability of the cost into account. It contains as a special case the classical risk-sensitive optimization criterion with an exponential utility. We show that this optimization problem can be solved by an ordinary MDP with extended state space and give conditions under which an optimal policy exists. In the case of an infinite time horizon we show that the minimal discounted cost can be obtained by value iteration and can be characterized as the unique solution of a fixed point equation using a 'sandwich' argument. Interestingly, it turns out that in case of a power utility, the problem simplifies and is of similar complexity than the exponential utility case, however has not been treated in the literature so far. We also establish the validity (and convergence) of the policy improvement method. A simple numerical example, namely the classical repeated casino game is considered to illustrate the influence of the certainty equivalent and its parameters. Finally also the average cost problem is investigated. Surprisingly it turns out that under suitable recurrence conditions on the MDP for convex power utility U , the minimal average cost does not depend on U and is equal to the risk neutral average cost. This is in contrast to the classical risk sensitive criterion with exponential utility.

We study portfolio optimization problems in which the drift rate of the stock is Markov modulated and the driving factors cannot be observed by the investor. Using results from filter theory, we reduce this problem to one with complete observation. In the cases of logarithmic and power utility, we solve the problem explicitly with the help of stochastic control methods. It turns out that the value function is a classical solution of the corresponding Hamilton-Jacobi-Bellman equation. As a special case, we investigate the so-called Bayesian case, i.e. where the drift rate is unknown but does not change over time. In this case, we prove a number of interesting properties of the optimal portfolio strategy. In particular, using the likelihood-ratio ordering, we can compare the optimal investment in the case of observable drift rate to that in the case of unobservable drift rate. Thus, we also obtain the sign of the drift risk.

We consider stochastic control problems with jump-diffusion processes and formulate an algorithm which produces, starting from a given admissible control π, a new control with a better value. If no improvement is possible, then π is optimal. Such an algorithm is well-known for discrete-time Markov Decision Problems under the name Howard's policy improvement algorithm. The idea can be traced back to Bellman. Here we show with the help of martingale techniques that such an algorithm can also be formulated for stochastic control problems with jump-diffusion processes. As an application we derive some interesting results in portfolio optimization.

A financial market with one bond and one stock is considered where the risk free interest rate, the appreciation rate of the stock and the volatility of the stock depend on an external finite state Markov chain. We investigate the problem of maximizing the expected utility from terminal wealth and solve it by stochastic control methods for different utility functions. Due to explicit solutions it is possible to compare the value function of the problem to one where we have constant (average) market data. The case of benchmark optimization is also considered.