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Criticalidade e processos estocásticos na economia
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A ocorrência de quedas abruptas de grande amplitude nos mercados financeiros difíceis de reproduzir, segundo os modelos globalmente aceites, é um fenómeno já reportado há alguns anos[6]. No sentido de o explicar, partimos do fundamento das relações económicas entre os agentes, para construir as interacções microscópicas do sistema. Assumir este mecanismo, permite-nos abandonar o pressuposto associado aos processos estocásticos, que dominam os modelos actuais, de que a economia equivale a um sistema termodinâmico em equilíbrio, para podermos assumir que é um sistema aberto onde os diferentes agentes formam ligações entre si. Tomando em conta que os agentes económicos se organizam em redes complexas, mostramos que um sistema com tais interacções só existe num estado crítico. Consequentemente, eventos extremos de grande amplitude têm uma probabilidade não desprezável de ocorrer. Mostramos ainda que a incorporação de primeiros princípios da economia permite ao modelo reproduzir leis de potência semelhantes àquelas que são observadas nos mercados financeiros reais e que os expoentes observados dependem linearmente dos expoentes das redes complexas subjacentes. Argumentamos assim que, ao contrário de algumas correntes económicas, a economia não é um sistema fechado em equilíbrio termodinâmico, mas sim um sistema aberto num estado estacionário crítico auto-organizado.
The occurrence of huge drops on financial markets that are not explained by the general accepted models is a well reported phenomenon[6]. With the purpose of explaining it, we based ourselves on the reasons for an economic relation between agents to establish the microscopic interactions within the system. Assuming the existence of this mechanism, we can drop all the assumptions on which the stochastic processes that are used in the current models are based, namely that the economy is equivalent to a system in thermodynamic equilibrium, and assume that it is an open system where the different agents interact between them. Assuming that the economic agents are organized in complex networks, we show that a system with those interactions only exists in a critical state. Consequently, extreme events with large magnitude have a significant probability of occurrence. We also show that using economic first principles, our model reproduces power laws identical to those that are observed on the real markets and the observed exponents depend linearly from the exponent of the underlying complex network. We argue that, on opposition to some economic theories, the economy is not a closed system on thermodynamic equilibrium but as open system on stationary self-organized critical state.
The occurrence of huge drops on financial markets that are not explained by the general accepted models is a well reported phenomenon[6]. With the purpose of explaining it, we based ourselves on the reasons for an economic relation between agents to establish the microscopic interactions within the system. Assuming the existence of this mechanism, we can drop all the assumptions on which the stochastic processes that are used in the current models are based, namely that the economy is equivalent to a system in thermodynamic equilibrium, and assume that it is an open system where the different agents interact between them. Assuming that the economic agents are organized in complex networks, we show that a system with those interactions only exists in a critical state. Consequently, extreme events with large magnitude have a significant probability of occurrence. We also show that using economic first principles, our model reproduces power laws identical to those that are observed on the real markets and the observed exponents depend linearly from the exponent of the underlying complex network. We argue that, on opposition to some economic theories, the economy is not a closed system on thermodynamic equilibrium but as open system on stationary self-organized critical state.
Descrição
Tese de mestrado em Engenharia Física, apresentada à Universidade de Lisboa, através da Faculdade de Ciências, 2010
Palavras-chave
Engenharia Física Teses de mestrado - 2010