This work evaluates the performance of green exchange-traded funds (ETFs) using the expected utility, entropy and variance (EU-EV) risk model. Data from 14 green ETFs analysed in earlier literature in the in-sample period from January 2008 to December 2010 are used. The green ETFs are ranked according to their risk, considering the returns’ expected utility, entropy and variance, and the best-ranked ETFs are se...
This paper proposes a multi-risk criteria assessment methodology that can be used for air quality assessment. The method consists first in evaluating the risk for a given set of alternatives with different risk measures and then in applying multi-criteria decision making methods to determine the final risk assessment. As risk criteria the risk measures: mean, standard deviation, loss probability, value at risk,...
Neste livro, escrito para os estudantes de cursos de Matemática Aplicada, Física e Engenharia, a ênfase é dada ao aspeto geométrico da Álgebra Linear. Embora a maior parte do seu conteúdo seja voltada para quem inicia o estudo desta disciplina, leitores de níveis mais avançados também encontrarão aqui ligações importantes entre a Álgebra Linear e outras áreas da Matemática.
This paper proposes a risk assessment methodology for evaluating the surface water quality of hydrological basins. It is shown that the methodology can be used to determine the riskiest periods for water pollution in the year and to assess the risk of water sampling station clusters. The methodology consists first in determining the pollution risk implied by physico-chemical parameters (measured in different wa...
The purpose of this work is to explore the approach of K-means clustering for stock risk classification and efficient portfolio construction through a case study, using data from the PSI index from January 2019 to December 2022. The classification of stock risks will be based on the expected utility, entropy and variance (EU-EV) risk model. The methodology consists in ap-plying K-means clustering with EU-EV ris...
O matemático e filósofo Pitágoras foi um dos primeiros a dedicar-se ao estudo da relação entre a matemática e a música. Com o monocórdio descobriu relações entre intervalos musicais e proporções numéricas e desenvolveu o primeiro sistema de afinação — o sistema pitagórico — para construir a escala musical. No entanto este sistema não era consistente; pois, por exemplo, doze intervalos de quinta não correspondia...
Mathematics and Music are closely connected and their multifaceted relationship has been explored since ancient times. Pythagoras was one of the first who discovered and formalized one of those connections by studying the arithmetic of musical intervals, expressing them by numerical ratios and relating ratios to consonance/dissonance notions, being the Pythagorean tuning and scale based on arithmetic principles...
In this paper, the performance of portfolios consisting of stocks selected with the recently proposed expected utility, entropy and variance (EU-EV) risk model is analysed. The portfolios were constructed using data of the PSI 20 index, from January 2019 to December 2020, by reducing the number of stock components to the half with the EU-EV risk model. The effciency of these portfolios in terms of the mean-vari...
In the context of investment decision-making, the selection of stocks is important for a successful construction of portfolios. In this paper the expected utility, entropy and variance (EU-EV) model is applied for stock selection, which can be used as preselection model for mean-variance portfolio optimization problems. Based on the EU-EV risk, stocks are ranked and the best ranked stocks with lower risk are se...
In this work we show how concepts and methods from actuarial risk theory can be applied to risk analysis in industry. Risk analysis consists in identifying, quantifying and classifying or ordering risks. In the proposed methodology, the risks identified in industrial setting, are modeled by loss random variables. The loss random variables are used to calculate the expected loss, the loss variance and exceedance...