A carregar...
Publicação
Transformação de geometria de redes complexas para espaços lineares usando observadores comóveis
| Nome: | Descrição: | Tamanho: | Formato: | |
|---|---|---|---|---|
| 1.94 MB | Adobe PDF |
Autores
Resumo(s)
Dois conceitos fundamentais em Finanças são o ativo e o passivo de uma entidade. O que tenho (ativo) e o que devo (passivo) são conceitos que fazem parte do senso comum e acredita-se que são indicadores da “saúde económica” de empresas e indivíduos. Assim, muitas foram as tentativas de extrair informações e previsões destes valores económicos. No entanto, “medir a economia” é um desafio que não deve ser menosprezado. Se é fácil saber a quantidade de moeda em circulação, esta é apenas uma representação da economia; o que nos interessa medir verdadeiramente são as trocas de bens e serviços e o “trabalho” que as tornou possíveis (aqui, trabalho refere-se ao conceito humano de trabalhar em vez do usado na física). –Junta-se a isto a natureza altamente confidencial e pessoal de todos os dados económicos. Um ponto que tem sido especialmente difícil de ultrapassar, e que muitas vezes é desprezado em análises económicas, é que a distribuição de uma variável económica (riqueza, dívida, rendimentos, etc) não é Gaussiana. De facto, a variância destas distribuições é muitas vezes infinita, ganhando por isso a designação de distribuições heavy-tail na literatura económica. O facto da variância ser infinita invalida a aplicação do Teorema do Limite Central (TLC), o que significa que o valor dos momentos não converge com o aumento da quantidade de dados. O presente documento estabelece um algoritmo de transformação que, aplicado a uma distribuição com variância infinita a transforma em finita. Para fundamentar esta transformação partimos de um modelo simples inspirado pela “expansão do espaço económico”, fundamentado com dados estatísticos de vários países recolhidos ao longo de várias décadas. Esta análise indica que é possível normalizar uma distribuição heavy-tail e também que é necessária uma análise extra na comparação de diferentes instantes de tempo. Levamos este estudo um pouco mais longe para modelar também o efeito da inflação económica. A monitorização e controlo deste fenómeno é um dos pontos mais comuns em programas eleitorais, em declarações de missão de entidades internacionais ou em listagens de serviços de consultoras mundiais. Usando conceitos de teoria de grafos conseguimos expandir a análise inicial para o eixo do tempo. Este último passo da transformação permite aumentar os dados disponíveis que, tendo já sido normalizados para variância finita, servem para melhorar a estatística no estudo da Economia e dos agentes e sistemas que a compõe.
Two fundamental concepts in Finance are the assets and the liabilities of a certain entity. What I have (assets) and what I owe (liabilities) are concepts present within common sense and believed to be an indication of “economic health” of companies and individuals. Many have attempted to extract information and obtain predictive power from these economic values, but actually, “measuring the economy” is a challenge in and of itself. While it is easy to know the amount of currency in circulation, that is just a representation of the economy. What we truly want to measure are the trades of goods and services, along with the “work” (here we use the human concept, not the physics one) that created them in the first place. –On top of this we have the highly confidential and personal nature of the data in question. A difficult point to overcome that has been downplayed in most literature is that the distributions of an economic variable (wealth, debt, income, etc.) are usually non-Gaussian. In fact, the variance of these distributions is usually infinite, which has earned them the classification of heavy-tail distributions in economic literature. With infinite variance the applicability of the Central Limit Theorem is highly impaired which means more data will not necessarily help. In fact, the value of statistical moments does not converge with the increase of statistical data. This text sugests a transformation algorithm that, when applied to a distribution with non-finite variance will map it into one with finite variance. To justify the steps taken we will start from a simple model inspired by the expansion of the economic universe, and emboldened by statistical data from several countries over several decades. This analysis also indicates that it is indeed possible to normalize a heavy-tail distribution and an extra step is required when comparing different points in time. We will take this model a bit further by looking the effects of inflation. Monitoring and controlling this phenomenon is a prevailing point in electoral programs, mission statements of international entities, service offered by world-wide consulting firms. Using ideas and methods from graph theory we are able to expand our initial analysis to the time axis. This will greatly increase the amount of data available to study the Economy and the systems that are part of it.
Two fundamental concepts in Finance are the assets and the liabilities of a certain entity. What I have (assets) and what I owe (liabilities) are concepts present within common sense and believed to be an indication of “economic health” of companies and individuals. Many have attempted to extract information and obtain predictive power from these economic values, but actually, “measuring the economy” is a challenge in and of itself. While it is easy to know the amount of currency in circulation, that is just a representation of the economy. What we truly want to measure are the trades of goods and services, along with the “work” (here we use the human concept, not the physics one) that created them in the first place. –On top of this we have the highly confidential and personal nature of the data in question. A difficult point to overcome that has been downplayed in most literature is that the distributions of an economic variable (wealth, debt, income, etc.) are usually non-Gaussian. In fact, the variance of these distributions is usually infinite, which has earned them the classification of heavy-tail distributions in economic literature. With infinite variance the applicability of the Central Limit Theorem is highly impaired which means more data will not necessarily help. In fact, the value of statistical moments does not converge with the increase of statistical data. This text sugests a transformation algorithm that, when applied to a distribution with non-finite variance will map it into one with finite variance. To justify the steps taken we will start from a simple model inspired by the expansion of the economic universe, and emboldened by statistical data from several countries over several decades. This analysis also indicates that it is indeed possible to normalize a heavy-tail distribution and an extra step is required when comparing different points in time. We will take this model a bit further by looking the effects of inflation. Monitoring and controlling this phenomenon is a prevailing point in electoral programs, mission statements of international entities, service offered by world-wide consulting firms. Using ideas and methods from graph theory we are able to expand our initial analysis to the time axis. This will greatly increase the amount of data available to study the Economy and the systems that are part of it.
Descrição
Tese de mestrado integrado, Engenharia Física, Universidade de Lisboa, Faculdade de Ciências, 2021
Palavras-chave
Economia Heavy-tail Teorema do Limite Central Distribuição de Pareto Lei de Potência Redes Complexas Valor do Dinheiro Empresas Portuguesas Teses de mestrado - 2021