The Exact Value for European Options on a Stock Paying a Discrete Dividend

In the context of a Black-Scholes economy and with a no-arbitrage argument, we derive arbitrarily accurate lower and upper bounds for the value of European options on a stock paying a discrete dividend. Setting the option price error below the smallest monetary unity, both bounds coincide, and we obtain the exact value of the option.Comment: 14 pages,3 figure

Enquadramento de um Treinador Adjunto com funções de Fisiologista relacionando a Equipa Técnica e o Benfica Lab

Orientador: Professor Doutor Nuno Alexandre Paulo LoureiroResumo O estágio relatado neste documento é relativo ao Mestrado em Desporto, com especialização em Treino Desportivo, na Modalidade de Futebol. Este relatório de estágio contempla os dois momentos de formação, o Estágio realizado no Sport Lisboa e Benfica, diretamente inserido na estrutura profissional do Benfica LAB e pertencente à equipa técnica de Sub-17, participantes no Campeonato Nacional de Juniores B, onde se reflete sobre as tarefas e funções realizadas durante o período de estágio, e o Estudo onde foi efetuada uma investigação tendo como principal objetivo a “Relação entre os Testes Físicos e as Posições de Campo, numa Academia de Elite em Futebol”. Os principais resultados obtidos por este estudo foram diferenças significativas que permitem afirmar que os Guarda-Redes são os jogadores menos resistentes, mas também são, em conjunto com os Defesas-Laterais os menos rápidos em testes de Velocidade acima de 15 metros. No entanto os Médios-Ala e os Defesas-Laterais são os jogadores mais resistentes, sendo que os MédiosAla são jogadores mais rápidos e mais explosivos.Abstract The curricular internship reported in this document is related to the Master in Sports Degree, with specialization in Sports Training, in Football (Soccer). This internship report covers the two most important themes, the Internship held at Sport Lisboa e Benfica, directly inserted in the professional structure of Benfica LAB and belonging to the U-17 technical team, participating in the National Championship of Juniors B, where it is reflected on the tasks and actions carried out during this period and the Study where an investigation was carried out having as main objective the "Relationship between Physical Tests and Field Positions in an Elite Football Academy". The results obtained by this study has showed us significant differences that allow to affirm that the Goalkeepers are the less resistant players, but also are, as the Full Backs the less rapid in tests of Speed above 15 meters. However, the Wingers and the Full Backs are the toughest players, and the Wingers are the fastest and more explosive players.N/

Context-Oriented Algorithmic Design

Currently, algorithmic approaches are being introduced in several areas of expertise, namely Architecture. Algorithmic Design (AD) is an approach for architecture that takes advantage of algorithms to produce complex designs, to simplify the exploration of variations, or to mechanize tasks, including those related to analysis and optimization of designs. However, architects might need different models of the same design for different kinds of analysis, which tempts them to extend the same code base for different purposes, typically making the code brittle and hard to understand. In this paper, we propose to extend AD with Context-Oriented Programming (COP), a programming paradigm based on context that dynamically changes the behavior of the code. To this end, we propose a COP library and we explore its combination with an AD tool. Finally, we implement two case studies with our context-oriented approach, and discuss their advantages and disadvantages when compared to the traditional AD approach