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This paper investigates the optimal management of an aggregated defined benefit pension plan in a stochastic environment. The interest rate follows the Ornstein-Uhlenbeck model, the benefits follow the geometric Brownian motion while the contribution rate is determined by the spread method of fund amortization. The pension manager invests in the financial market with three assets: cash, a zero-coupon bond and a stock. Regardless of the initial status of the plan, we suppose that the pension fund may become underfunded or overfunded in the planning horizon. The optimization goal of the manager is to maximize the expected utility in the overfunded region minus the weighted solvency risk in the underfunded region. By introducing an auxiliary process and related equivalent optimization problems and using the martingale method, the optimal wealth process, optimal portfolio and efficient frontier are obtained under four cases (high tolerance towards solvency risk, low tolerance towards solvency risk, a specific lower bound, and high lower bound). Moreover, we also obtain the probabilities that the optimal terminal wealth falls in the overfunded and underfunded regions. At last, we present numerical analyzes to illustrate the manager's economic behaviors. [ABSTRACT FROM AUTHOR]

The main of the study is to comprehend how the mean variance efficient frontier method may be used in conjunction with Markowitz portfolio theory to produce an optimal portfolio. The study uses daily observations 8 pharma companies closing price namely Auropharma, Granules, Glaxo, Lauruslabs, Pfizer, Sanofi and Torntpharma. Further, Nifty pharma index is considered as benchmark index to check the performance of the chosen companies. The study chosen the reference period from 2020 to 2023 and required data has been extracted from the National Stock Exchange (NSE). This research is based on implementing a stochastic method for efficient portfolio optimisation employing a blended Monte Carlo and Markowitz model. In order to forecast the price of these indices in the future and to determine the likelihood of profit or loss while investing in a portfolio of stocks representing the aforementioned indices, the study also uses Monte Carlo simulation. The study involves two algorithms, namely the deterministic optimisation algorithm, which uses Markowitz Portfolio Theory, and the probabilistic optimisation algorithm, which uses Monte Carlo simulation. The study employed correlation matrix to find the exist relationship between the chosen companies and benchmark index. Also, expected return and volatility has been identified with the help of standard deviation using Python. The study found that the NIFTY Pharma index offers a higher return of 14.35. In addition to this, NIFTY Pharma portfolio's volatility is considerably higher. The study concludes that the NIFTY pharma portfolio is more suitable for those investors who have an appetite for risk. [ABSTRACT FROM AUTHOR]

This survey offers a succinct overview of the General Framework of Portfolio Theory (GFPT), consolidating Markowitz portfolio theory, the growth optimal portfolio theory, and the theory of risk measures. Central to this framework is the use of convex analysis and duality, reflecting the concavity of reward functions and the convexity of risk measures due to diversification effects. Furthermore, practical considerations, such as managing multiple risks in bank balance sheets, have expanded the theory to encompass vector risk analysis. The goal of this survey is to provide readers with a concise tour of the GFPT's key concepts and practical applications without delving into excessive technicalities. Instead, it directs interested readers to the comprehensive monograph of Maier-Paape, Júdice, Platen, and Zhu (2023) for detailed proofs and further exploration. [ABSTRACT FROM AUTHOR]

In this study, we investigate the connection between the efficient frontier (EF) of a general multiobjective mixed integer linear optimization problem (MILP) and the so-called restricted value function (RVF) of a closely related single-objective MILP. In the first part of the paper, we detail the mathematical structure of the RVF, including characterizing the set of points at which it is differentiable, the gradients at such points, and the subdifferential at all nondifferentiable points. We then show that the EF of the multiobjective MILP is comprised of points on the boundary of the epigraph of the RVF and that any description of the EF suffices to describe the RVF and vice versa. Because of the close relationship of the RVF to the EF, we observe that methods for constructing the so-called value function (VF) of an MILP and methods for constructing the EF of a multiobjective optimization problem are effectively interchangeable. Exploiting this observation, we propose a generalized cutting-plane algorithm for constructing the EF of a multiobjective MILP that arises from an existing algorithm for constructing the classical MILP VF. The algorithm identifies the set of all integer parts of solutions on the EF. We prove that the algorithm converges finitely under a standard boundedness assumption and comes with a performance guarantee if terminated early. [ABSTRACT FROM AUTHOR]

Pension funds’ investments are increasingly linked to the changes in climate and environmental protection. The integration of environmental, social and governance (ESG) factors into their investment process is still varying in different countries and regions. The limited number of studies on the application of the ESG investment approach by private pension funds in Bulgaria shows that the country lags behind the trends in Europe. Although pension funds do not perceive environmental investments as riskier or less profitable than conventional ones, many of them remain cautious due to the shorterterm financial performance data of green assets. To achieve adequate retirement savings and a high replacement rate saving “more and for longer” is not enough. As far as the topic of portfolio investment performance is on the agenda, one would reasonably ask what the reflection of environmental investments would be on the widely diversified portfolios of pension funds in the country. The present research is dedicated to а mean-variance (MV) portfolio optimization involving a selection of conventional and green assets under different constraints and “shades of green” by using historical data. The empirical results from the portfolio optimizations performed shed light on the questions raised and complement the motivational spectrum “in favour of” or “against” environmental investment. [ABSTRACT FROM AUTHOR]

In this paper, we design a neural network architecture to approximate the weakly efficient frontier of convex vector optimization problems (CVOP) satisfying Slater's condition. The proposed machine learning methodology provides both an inner and outer approximation of the weakly efficient frontier, as well as an upper bound to the error at each approximated efficient point. In numerical case studies we demonstrate that the proposed algorithm is effectively able to approximate the true weakly efficient frontier of CVOPs. This remains true even for large problems (i.e., many objectives, variables, and constraints) and thus overcoming the curse of dimensionality. [ABSTRACT FROM AUTHOR]

This paper investigates sectoral diversification within Borsa Istanbul, aiming to elucidate its impact on portfolio risk and return dynamics. Spanning the timeframe from 2020 to 2022, the study meticulously analyzes stocks from pivotal sectors, including banking, energy, and iron and steel. Employing a robust methodology, the research harnesses Monte Carlo simulations to generate many hypothetical portfolios, subsequently evaluating them on the Efficient Frontier to identify optimal risk-return tradeoffs. Key performance metrics, such as the Sharpe Ratio, Sortino Ratio, and Maximum Drawdown, further enrich the analysis, providing a granular view of portfolio behaviors. The significance of this study lies in its bridging of theoretical constructs of diversification with the tangible realities of an emerging market like Borsa Istanbul. Our main findings underscore the potential benefits of sectoral diversification while highlighting the complexities inherent in portfolio construction. The insights gleaned offer valuable guidance for investors, emphasizing the delicate balance between risk mitigation and return optimization in a diversified portfolio. [ABSTRACT FROM AUTHOR]

We consider a situation in which two parties have concluded an efficient contract corresponding to one major bargaining solution. After the parties have agreed on one particular contract, an unanticipated shock may change the contract outcomes in a way that benefits one party but harms the other party. If this happens, they have the option to either stay with the original exchange contract or adjust some contract parameters such as the price. We propose a model to perform such adjustments automatically, to obtain the same bargaining solution as in the initial contract under the restriction that the new contract dominates the outcomes of the original contract. We study several bargaining solutions within this general framework. These bargaining solutions offer various sharing rules to distribute the benefit between the parties. To reflect practical considerations, we only consider adjustments made via one contract parameter (the price), while all other parameters result from the original contract and the random shock. To evaluate the efficiency of the proposed approach, we also compare it to a full re-negotiation scenario, in which all parameters can be modified within the boundaries resulting after the random shock. However, waiting and re-negotiation might be costly compared to the situation when the smart contract executes the adjustment automatically. Therefore, the automatic adjustment might be more efficient compared to the other types of contracts. We present several numerical examples and run large random simulations, which we also check statistically. [ABSTRACT FROM AUTHOR]

Researchers traditionally compute isolated points for an efficient frontier and assume a line which passes through a risk-free asset r f and is tangent to the frontier. The tangency plays pivotal roles for the capital asset pricing model (CAPM). However, the assumption may not hold in the presence of kinks (as non-differentiable points) on efficient frontiers. Kinks are detected by parametric-quadratic programming only and not by ordinary portfolio optimization. Up until now, there has been no research to theoretically scrutinize kink properties (especially implications to CAPM) and systematically quantify the nonexistence of the tangency. In such an area, this paper contributes to the literature. In theorems and corollaries, we prove the nonexistence of the tangency and substantiate that expected-return axis is composed of piecewisely connected intervals for which the tangency does not exist and intervals for which the tangency exists. Computationally, we reveal universal existence of kinks (e.g., 0.2 to 8.0 kinks for 5-stock to 1800-stock portfolio selections) and the tangency-nonexistence ratios as about 0.066. [ABSTRACT FROM AUTHOR]

Here we have proposed fuzzy portfolio selection model using stochastic correlation (FPSMSC) to overcome limitations both in fuzzy and stochastic world. The newly proposed model not only gets harmonious efficient frontier, but also considers the future movement of stock prices based on fuzzy expertise knowledge. The investment weights of the model have been optimized based on the monthly return data of 18 stocks listed in S&P500 from October 2011 to September 2015. The proposed model has provided higher returns in the whole regime of risk for the period from October 2014 to September 2015, whose monthly return data are used as training data than other available portfolio selection models, i.e., fuzzy portfolio selection models with credibility and possibility and statistic model. Also, the present model has shown the better smoothness of the variations of returns with respect to risk aversion parameter, λ, from the monthly data from October 2015 to September 2016, which is not included to training database. Especially, our model is superior to other models in the regime of 0–0.3 for the risk aversion level. It is demonstrating that the FPSMSC is efficient for the investors who tend to seek the high return in portfolio management. [ABSTRACT FROM AUTHOR]

Over the years several studies have reported a significant waste of advertising budget, a finding which calls for strategies to increase advertising efficiency. While some factors, such as brand extensions or an optimal marketing mix, have already been identified as relevant determinants of advertising efficiency, changes in consumer psychographics have so far been neglected. The current study fills this gap by investigating how the emerging awareness and demand for corporate sustainability serve as a contextual factor leveraging or hindering advertising efficiency. Furthermore, we investigate how advertising efficiency has changed across various industry sectors from 2010 to 2019. A two-step procedure was applied to analyze the secondary data of 1950 observations from 195 US firms in five industry sectors over a period of 10 years. The resulting time series of firm-specific multi-directional efficiency scores confirms that advertising efficiency varies over time, justifying the relevance of a dynamic perspective for analyzing advertising efficiency. Furthermore, in support of our main claim, the investigation of the relationship between advertising efficiency and the environmental, social and governance performance of firms over time using a time-fixed effects panel regression and a three-level hierarchical regression model confirm the significant impact of corporate sustainability performance on advertising efficiency. Interestingly, this effect varies among different industry sectors and not all corporate sustainability activities impact advertising efficiency to the same extent. The results not only emphasize the relevance of corporate sustainability performance in increasing advertising efficiency, but also guide marketers on strategic marketing decisions related to the allocation of advertising budget. [ABSTRACT FROM AUTHOR]

Copyright of Operations Research Transactions / Yunchouxue Xuebao is the property of Editorial office of Operations Research Transactions and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Models with selective convexity are an important class of data envelopment analysis (DEA) models. This type of model allows managers to consider variables such as ratios, averages, percentages, etc. The paper proposes algorithms for constructing input and output isoquants using volume variables in models with selective convexity. These algorithms help investigate the relationship between any volume variables in the model. Computational experiments confirm the reliability and efficiency of the proposed methods. [ABSTRACT FROM AUTHOR]

In this study, we deal with a portfolio optimization problem including both risky and risk-free assets. We use the infinity norm criterion to measure portfolio risk and formulate the problem as a bi-objective linear optimization problem. Then, a single objective linear program is considered related to the bi-objective optimization problem. Using the well-known Karush-Kuhn-Tucker optimality conditions, we obtain analytic formula for an optimal solution. Moreover, we determine the whole efficient frontier by multi-criteria optimization techniques. Based on the theoretical results, two algorithms are proposed for finding the portfolio weights and the efficient frontier. Numerical examples are given for illustrating the new models and algorithms. Additionally, a simulation study has been conducted to assess the performance of the proposed method. [ABSTRACT FROM AUTHOR]

The spread of COVID‐19 outbreak has promoted truck‐drone delivery from trials to commercial applications in end‐to‐end contactless solutions. To fully integrate truck‐drone delivery in contactless solutions, we introduce the robust traveling salesman problem with a drone, in which a drone makes deliveries and returns to the truck that is moving on its route under uncertainty. The challenge is to find, for each customer location in truck‐drone routing, an assignment to minimize the expected makespan. Apart from the complexity of this problem, the risk of synchronization failure associated with uncertain travel time should be also considered. The problem is first formulated as a robust model, and a novel efficient frontier heuristic is proposed to solve this model. By coupling the implicit adaptive weighting with epsilon‐constraint methods, the heuristic generates a series of scalarized single‐objective problems, where the goal is to minimize expected makespan under the constraint of synchronization risk. The experiment results show that the robust (near‐)optimal solutions offer a considerable reduction in risk, yet only hint at a small increase in makespan. The heuristic in the present study is effective to construct approximations of Pareto frontier and allows for assignment decisions in a priori or a posteriori manner. [ABSTRACT FROM AUTHOR]

This survey offers a succinct overview of the General Framework of Portfolio Theory (GFPT), consolidating Markowitz portfolio theory, the growth optimal portfolio theory, and the theory of risk measures. Central to this framework is the use of convex analysis and duality, reflecting the concavity of reward functions and the convexity of risk measures due to diversification effects. Furthermore, practical considerations, such as managing multiple risks in bank balance sheets, have expanded the theory to encompass vector risk analysis. The goal of this survey is to provide readers with a concise tour of the GFPT’s key concepts and practical applications without delving into excessive technicalities. Instead, it directs interested readers to the comprehensive monograph of Maier-Paape, Júdice, Platen, and Zhu (2023) for detailed proofs and further exploration.

This paper responds to the recent (2022) change to Regulation 28 of the South African Pension Funds Act which now permits an increased allocation (raised from 30% to 45%) in foreign investments. Our primary aim is to establish a strategic (long-term) benchmark weight for the allocation to foreign assets. Our secondary aim is to assist in building intuition on potential tactical (shorter-term) foreign allocation decisions. To ensure rigour in our study, we use a novel dataset dating back to the 1930s and we utilise methodologies in recent academic literature in the mean-variance framework. Our optimisation evidence supports a strategic foreign benchmark allocation of 39% (with 61% allocated to local asset classes). We highlight that this strategic foreign benchmark of 39% (probably for the first time) enables managers to potentially take on meaningful tactical overweight foreign positions. We establish that this strategic foreign benchmark would have reduced the risk (standard deviation of returns) of the local-only optimal portfolio significantly from 10% p.a. down to 8.7% p.a. over the 92 year period analysed, whilst increasing the return by an additional 1.1% p.a. over the local-only portfolio. Lastly, we provide guidance on tactical foreign allocation decisions based on four potential local economic regimes. [ABSTRACT FROM AUTHOR]

We propose a novel asset allocation model using a Markov process of states defined by clustered efficient frontier coefficients. While most research in Markov models of the market characterize regimes using return and volatility, we instead propose characterizing these states using efficient frontiers, which provide more information on the interactions of underlying assets that comprise the market. Efficient frontiers can be decomposed to their functional form, a square-root second-order polynomial defined by three coefficients, to provide a dimensionality reduction of the return vector and covariance matrix. Each month, the proposed model hierarchically clusters the monthly coefficients data up to the current month, to characterize the market states, then defines a Markov process on the sequence of states. To incorporate these states into portfolio optimization, for each state, we calculate the tangency portfolio using only return data in that state. We then take the expectation of theseweights for each state, weighted by the probability of transitioning from the current state to each state. To empirically validate our proposed model, we employ three sets of assets that span the market, and show that our proposed model significantly outperforms benchmark portfolios. [ABSTRACT FROM AUTHOR]

Copyright of Les Cahiers du CREAD is the property of Centre de Rrecherche en Economie Appliquee pour Developpement and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

The goal of this paper is to estimate the percentage structure of electricity generation by type of technology in Mexico for the period 1992-2016. Modern portfolio theory and the capital asset pricing model of Sharpe and Litner were used. Results show that using only portfolio theory is not possible to find non-negative percentages in all the technologies. When a risk-free asset is included, there is a region where all technologies have a positive participation in electricity generation. The efficient frontier is found at 20% for wind technology share and for the rest of technologies, shares are almost equally - distributed among them. [ABSTRACT FROM AUTHOR]

We propose a novel asset allocation model using a Markov process of states defined by clustered efficient frontier coefficients. While most research in Markov models of the market characterize regimes using return and volatility, we instead propose characterizing these states using efficient frontiers, which provide more information on the interactions of underlying assets that comprise the market. Efficient frontiers can be decomposed to their functional form, a square-root second-order polynomial defined by three coefficients, to provide a dimensionality reduction of the return vector and covariance matrix. Each month, the proposed model hierarchically clusters the monthly coefficients data up to the current month, to characterize the market states, then defines a Markov process on the sequence of states. To incorporate these states into portfolio optimization, for each state, we calculate the tangency portfolio using only return data in that state. We then take the expectation of these weights for each state, weighted by the probability of transitioning from the current state to each state. To empirically validate our proposed model, we employ three sets of assets that span the market, and show that our proposed model significantly outperforms benchmark portfolios.

There is a general consensus about the performance of photovoltaic plants particularly on their efficiency benefits. However, it is not clear to what extents such efficiencies correlate with the efficient frontier of performance when such plants are evaluated under varying geospatial environmental factors and over intertemporal periods. This study carries out a performance benchmarking exercise on photovoltaic power stations. It employs a non-parametric modelling technique in the form of Data Envelopment Analysis to evaluate the performance over time of three photovoltaic power plants within an electric utility. It presents an optimization modelling approach for performance benchmarking over time under situations where there are a limited number of decision-making units. Specifically, the study introduces a multi-period modeling approach which employs real data and captures actual variabilities in environmental factors that influence the output of photovoltaic power plants over time. In comparing the deterministic approach often employed in the extant literature with the multi-period model, the results reveal that the deterministic model overestimates the efficiency values and underestimates the output targets relative to a unit operating on the efficient frontier. The study further employs non-parametric statistical techniques and post-hoc tests to validate the findings. [ABSTRACT FROM AUTHOR]

We propose a novel model to achieve superior out-of-sample Sharpe ratios. While most research in asset allocation focuses on estimating the return vector and covariance matrix, the first component of our novel model instead forecasts the future tangency portfolio, and the second component then determines the optimal investment portfolio. First, to forecast the tangency portfolio, we forecast the efficient frontier by decomposing its functional form, a square root second-order polynomial, into three interpretable coefficients, which can then be used to calculate a forecasted tangency portfolio. These coefficients can be forecasted using vector autoregressions. Second, the model invests in the portfolio on the efficient frontier that is the minimum Euclidean distance from this forecasted tangency portfolio. A motivation for our approach is to address the limitation that the tangency portfolio only maximizes the Sharpe ratio when future returns and covariances are stationary, and can be directly estimated with historical data, which often does not hold in out-of-sample data. Our approach addresses this shortcoming in a novel way by forecasting the tangency portfolio, rather than estimating return and covariance. For empirical testing, we employ two sets of assets that span the market to demonstrate and validate the performance of this novel method. [ABSTRACT FROM AUTHOR]

This paper studies a continuous-time securities market where an agent, having a random investment horizon and a targeted terminal mean return, seeks to minimize the variance of a portfolio's return. Two situations are discussed, namely a deterministic time-varying density process and a stochastic density process. In contrast to [18], the variance of an investment portfolio is no longer minimal when all assets are invested in a risk-free security. Furthermore, the random investment horizon has a material effect on the efficient frontier. This provides some insights into the classical mutual fund theorem. [ABSTRACT FROM AUTHOR]

Since the future output of wind power generation is uncertain due to weather conditions, there is an increasing need to manage the risks associated with wind power businesses, which have been increasingly implemented in recent years. This study introduces multiple weather derivatives of wind speed and temperature and examines their effectiveness in reducing (hedging) the fluctuation risk of future cash flows attributed to wind power generation. Given the diversification of hedgers and hedging needs, we propose new standardized derivatives with higher-order monomial payoff functions, such as "wind speed cubic derivatives" and "wind speed and temperature cross-derivatives," to minimize the cash flow variance and develop a market-trading scheme to practically use these derivatives in wind power businesses. In particular, while demonstrating the importance of standardizing weather derivatives regarding market liquidity and efficiency, we propose a strategy to narrow down the required number (or volume) of traded instruments and improve trading efficiency by utilizing the least absolute shrinkage and selection operator (LASSO) regression. Empirical analysis reveals that higher-order, multivariate standardized derivatives can not only enhance the out-of-sample hedge effect but also help reduce trading volume. The results suggest that diversification of hedging instruments increases transaction flexibility and helps wind power generators find more efficient portfolios, which can be generalized to risk management practices in other businesses. [ABSTRACT FROM AUTHOR]

To test for arbitrage opportunities and market efficiency in the Hong Kong money, stock, and real estate markets, we find that the money market stochastically dominates both the stock and real estate markets. Furthermore, the real estate market dominates the stock market, the money market dominates nearly all the efficient frontier portfolios, none of the efficient portfolios dominates the money market, and the money market also dominates the equal-weighting portfolio. This infers that in some cases investors could achieve higher expected ex-ante utility by investing in an individual asset rather than a portfolio. Our conclusions drawn from the pre-COVID-19 period are the same as those drawn from the entire period and the conclusions drawn from the COVID-19 period are the same as those drawn from the entire period except that the money market only stochastically dominates some of the efficient frontier portfolios. Our findings question diversification benefits in the Hong Kong capital market during our sample period, including both the pre-COVID-19 and COVID-19 periods. [ABSTRACT FROM AUTHOR]

The two opposing investment strategies, diversification and concentration, have often been directly compared. While there is much less dispute regarding Markowitz's approach as the benchmark for diversification, the precise meaning of concentration in portfolio selection remains unclear. This paper offers a novel definition of concentration, along with an extreme value theory-based estimator for its implementation. When overlaying the performances derived from diversification (in Markowitz's sense) and concentration (in our definition), we find an implied risk threshold, at which the two polar investment strategies reconcile—diversification has a higher expected return in situations where risk is below the threshold, while concentration becomes the preferred strategy when the risk exceeds the threshold. Different from the conventional concave shape, the estimated frontier resembles the shape of a seagull, which is piecewise concave. Further, taking the equity premium puzzle as an example, we demonstrate how the family of frontiers nested inbetween the estimated curves can provide new perspectives for research involving market portfolios. [ABSTRACT FROM AUTHOR]

Under stress events, most of the asset prices tend to be positively correlated, breaking the diversification benefits. In this study, we explore the performance of different assets particularly during stress events (the 2008 crisis and the COVID-19 crisis) which can come to the rescue of portfolio managers as hedging strategies. Further, the analysis evaluates the performance of different combinations of portfolios with and without including volatility assets. Empirical results indicate that with only an allocation of 5% of the portfolio to volatility asset class, investors with different risk appetites were able to achieve 10% expected returns with reduced uncertainty.

It is well known that the models supporting the Modern Portfolio Theory (MPT) and the Efficient Market Hypothesis (EMH) are constructed in the framework of random walk theory. However, a large and growing literature criticizes those models. The Fractal Market Hypothesis (FMH) was proposed as an alternative hypothesis to EMH. The motivation of this study is Peters' [45,46] works that examine the portfolio selection case based on the non-normality framework. The aim of the study is to propose a new approach to theoretical framework of portfolio selection in terms of FMH. Daily observations of 92 stocks traded in London Stock Exchange are used to investigate the fractal behavior. Thus, the Hurst exponents as a means of indicator of a fractal structure are calculated for simulated portfolios. Results of the analysis show that the validity of MPT and EMH is questionable in London Stock Exchange. To examine the relationship between Hurst exponents (as a measure of risk) and returns, scattered diagrams are constructed for 5000 simulated portfolios. Existence of a pattern with a frontier is detected that may enable investors to optimize their portfolios. Further, The Hurst exponents of efficient frontier portfolios of Markowitz are calculated in order to investigate whether there is any linkage with the frontier of simulated portfolios. The results show that major deviations occur between these two frontiers. To understand these deviations, the Lyapunov exponents are suggested for detailed information. As a conclusion, it is recommended that investors should calculate an optimal solution with regards to the Hurst and Lyapunov exponents to maximize their returns. [ABSTRACT FROM AUTHOR]

Markowitz formulates portfolio selection and calls the optimal solutions as an efficient frontier. Sharpe initiates Sharpe ratio for frontier portfolios' reward to variability. Finance textbooks assume that there exists a line which passes through a risk-free rate and is tangent to an efficient frontier. The tangent portfolio enjoys the maximum Sharpe ratio. However, the assumption is over-simplistic because we prove that other situations exist. For example, Sharpe ratio itself may not be even well-defined. We comprehensively maximize Sharpe ratio. In such an area, this paper contributes to the literature. Specifically, we identify the other situations by parametric-quadratic programming which renders complete efficient frontiers by piecewise-hyperbola structure. Researchers traditionally view efficient frontiers by just isolated points. We accomplish handy formulae, so investors can even manually process them. The COVID-19 pandemic is unleashing crises. Unfortunately, there is quite limited research of portfolio selection for COVID. In such an area, this paper contributes to the practice. Specifically, we originate a counter-COVID measure for stocks and integrate it as a constraint into portfolio-selection models. The maximum-Sharpe-ratio portfolio outperforms stock-market indexes in sample. We launch the models for Dow Jones Industrial Average and discover outperformance out of sample. [ABSTRACT FROM AUTHOR]

Revenue management (RM) deals with selling the right product to the right customer at the right time at the right price through the right channel to maximise revenue. The innovation of RM lies in the way decisions are made. The performance of revenue management approaches can be evaluated against several criteria. Both discrete and continuous multicriteria models can be used to analyse RM. The performance pyramid is a comprehensive, fully integrated perperformance system that captures multiple perspectives such as internal, financial, customer and innovation. The assessment is based on a combination of Analytic Hierarchy Process (AHP), Analytic Network Process (ANP) and Data Envelopment Analysis (DEA) approaches. Customer behavior modeling is gaining increasing attention in revenue management. Customer choice models can be extended with more inputs and more outputs. Evaluation of alternatives can be performed using DEAbased evaluation methods. The search for an efficient frontier in a DEA model can be formulated as a multiobjective linear programming problem. We propose to use an Aspiration Level Oriented Procedure (ALOP) to solve the problem. [ABSTRACT FROM AUTHOR]

Orientation: Commodities are a prominent feature of the global economy. A substantial component of the income and welfare of both commodity-producing and commodity-consuming countries is highly dependent on the prices of commodities, such as metals. Metal prices are driven by economic growth and provide important insight into the state of the global economy: this behaviour is inextricably linked with the transitory shocks. Research purpose: Understanding recent metal price behaviour provides information about the economic implications of the coronavirus disease 2019 (COVID-19) pandemic as well as the Russia–Ukraine conflict. This research engages with the notion of the ongoing upward swing of the post-2000 super-cycle in the metals market. Motivation for the study: An analysis of metal price behaviour during COVID-19 and the Russia–Ukraine conflict describes the consequences of market shocks on commodity prices and examines the role played by super-cycles within metal markets. This work measures the optimal performances of portfolios comprising precious and nonprecious metals. Research approach/design and method: Portfolio optimisation using Lagrangian calculus under various constraints. The article argues that transitory shocks from pandemics and conflicts have a positive relationship with risk–return profiles of relevant portfolios. Main findings: A positive correlation was found between transitory shocks and prices of both precious and nonprecious metals. There is also evidence regarding the continuation of the post-2000 super-cycle in the metals market. Practical/managerial implications: Better knowledge of these relationships allows commodity traders to confidently assert that metal commodities will deliver healthy returns at moderate risk levels during periods that are characterised by different transitory shocks. Metals exist and exhibit safe haven properties during periods governed by economic uncertainty. Contribution/value add: Metals have exhibited strong economic performances in an economic landscape where little has flourished. This consequently affirms their importance and outlines their investment viability during volatile and uncertain periods.

Principal components analysis (PCA) is a well-known statistical method used to analyze the covariance structure of a random vector and for dimension reduction. When applied to an N-dimensional random vector of asset returns, PCA produces a set of N principal components, linear functions of the asset return vector that are mutually uncorrelated and which have some important statistical properties. The purpose of this paper is to consider the properties of portfolios based on such principal components, know as PC portfolios, including the efficiency of PC portfolios, the use of PC portfolios to reduce the return variance of a given portfolio, and the properties of factor models with PC portfolios as factors. [ABSTRACT FROM AUTHOR]

• The efficient frontier is generalized by adding the degree of responsibility as a third axis • Adding ESG uncertainty in the responsible investor's allocation mostly impacts low risk portfolios • Adding ESG uncertainty in the responsible investor's allocation is more substantial for high levels of responsibility The impact of ESG score uncertainty on the risk-return profile of socially responsible optimal portfolios is analyzed. Focusing on the 109 largest French company stock prices between 2021 and 2024, uncertainty about ESG score is measured through the lens of investors' assessment rather than from ESG rating agencies. The efficient frontier is generalized by introducing the degree of investors' social responsibility to the classic Markowitz approach. Our results show that taking into account ESG uncertainty substantially degrades the trade-off between portfolio return and volatility for highly responsible and low-risk portfolios. [ABSTRACT FROM AUTHOR]