Application of gauge theory to finance: a systematic literature review

In this dissertation, a systematic literature review was undertaken, exploring the application of gauge theory, an important formalism in physics literature, to finance. A set of keywords pertaining both gauge theory and finance were established and used as a search string in the database Web of Science. After exclusion and inclusion principles were applied to the set of articles generated, 14 papers were obtained. By systematically reviewing them, three major approaches to a financial gauge theory were found: Beliefs-Preferences Gauge Symmetry, Local Num´eraire Gauge Symmetry, and Deflator-Term Structure Gauge Symmetry. These can be essentially differentiated by the kind of gauge symmetry explored. Changing pairs of beliefs and preferences, local num´eraires and pairs of deflator and term structure is argued to be of no consequence to the dynamics of the financial market under consideration. A differential geometric treatment of financial markets as fibre bundles was shown to be necessary for an understanding of the gauge theory application, and proved itself to be successful in rethinking certain concepts, such as gains from arbitrage opportunities, being equivalent to the curvature of the said fibre bundle, an invariant under gauge transformations. The local num´eraire gauge symmetry turned out to be the most investigated one, leading to the execution of various numerical simulations, each with different added variations. Amongst them, the idea of using path integrals, a formalism from quantum mechanics, as a way of simulating the log price probability distributions of a market is used. This works by assuming that the market is characterized by the minimization of arbitrage opportunities. It was found good agreement with historical data, which substantiates the existence of gauge symmetry in financial markets, at least to some extent.Nesta dissertação de mestrado foi realizada uma revis˜ao sistem´atica da literatura, visando investigar a aplicação de teorias de gauge no contexto financeiro. Para este fim, foi constru´ıdo um conjunto de palavras-chave, pertinentes tanto em financ¸as como em teorias de gauge, subsequentemente introduzidas na base de dados Web of Science, com o intuito de encontrar todos os artigos que de alguma maneira as abordem. Princ´ıpios de exclusão e inclusão foram aplicados ao conjunto de artigos previamente obtido, traduzindo-se em 14 artigos considerados pertinentes. Revendo-os de modo sistemático, conclui-se que trˆes abordagens para uma teoria de gauge financeira podem ser destiladas: Simetria de Gauge Crenc¸as-Preferˆencias, Simetria de Gauge Num´eraire local, e Simetria de Gauge Deflator-Termo de Estrutura. Estas diferem no g´enero de simetria de gauge explorada. Alterações que afectem pares de crenc¸as e preferˆencias, num´eraire locais e pares de deflatores e termos de estrutura, assumem-se de nenhuma consequˆencia no que diz respeito `as dinˆamicas do mercado financeiro em considerac¸ ˜ao. Para um entendimento de teorias de gauge, provou-se necess´ario um tratamento geom´etrico de mercados financeiros, inspirado pelo formalismo de geometria diferencial, interpretando-os como um feixe de fibras. Tal tratamento matem´atico permite a reconceptualizac¸ ˜ao de ganhos ocorridos por usufruir de oportunidades de arbitragem como elementos do tensor de curvatura do feixe de fibras. Esta quantidade ´e dita invariante perante transformac¸ ˜oes de gauge. A simetria de gauge associada a escolhas locais de num´eraire revelou-se a abordagem mais investigada, levando `a execuc¸ ˜ao de diversas simulac¸ ˜oes num´ericas, cada uma com adic¸ ˜oes ´unicas ao modelo base. A ideia de usar integrais de caminho, um formalismo comum em mecˆanica quˆantica, de maneira a simular as distribuic¸ ˜oes de probabilidades do logaritmo de prec¸os caracter´ısticos de um mercado financeiro serviu de modelo base. Tal modelo baseia-se na assunc¸ ˜ao de que um mercado financeiro ´e caracterizado por minimizar os poss´ıveis ganhos associados a oportunidades de arbitragem. Demonstrou-se uma boa concordˆancia entre dados hist´oricos, relativo aos prec¸os de diversos activos, substanciando a ideia fundamental de que simetria de gauge existe em mercados financeiros

Pervasive gaps in Amazonian ecological research

Biodiversity loss is one of the main challenges of our time,1,2 and attempts to address it require a clear un derstanding of how ecological communities respond to environmental change across time and space.3,4 While the increasing availability of global databases on ecological communities has advanced our knowledge of biodiversity sensitivity to environmental changes,5–7 vast areas of the tropics remain understudied.8–11 In the American tropics, Amazonia stands out as the world’s most diverse rainforest and the primary source of Neotropical biodiversity,12 but it remains among the least known forests in America and is often underrepre sented in biodiversity databases.13–15 To worsen this situation, human-induced modifications16,17 may elim inate pieces of the Amazon’s biodiversity puzzle before we can use them to understand how ecological com munities are responding. To increase generalization and applicability of biodiversity knowledge,18,19 it is thus crucial to reduce biases in ecological research, particularly in regions projected to face the most pronounced environmental changes. We integrate ecological community metadata of 7,694 sampling sites for multiple or ganism groups in a machine learning model framework to map the research probability across the Brazilian Amazonia, while identifying the region’s vulnerability to environmental change. 15%–18% of the most ne glected areas in ecological research are expected to experience severe climate or land use changes by 2050. This means that unless we take immediate action, we will not be able to establish their current status, much less monitor how it is changing and what is being lostinfo:eu-repo/semantics/publishedVersio

Pervasive gaps in Amazonian ecological research

Biodiversity loss is one of the main challenges of our time,1,2 and attempts to address it require a clear understanding of how ecological communities respond to environmental change across time and space.3,4 While the increasing availability of global databases on ecological communities has advanced our knowledge of biodiversity sensitivity to environmental changes,5,6,7 vast areas of the tropics remain understudied.8,9,10,11 In the American tropics, Amazonia stands out as the world's most diverse rainforest and the primary source of Neotropical biodiversity,12 but it remains among the least known forests in America and is often underrepresented in biodiversity databases.13,14,15 To worsen this situation, human-induced modifications16,17 may eliminate pieces of the Amazon's biodiversity puzzle before we can use them to understand how ecological communities are responding. To increase generalization and applicability of biodiversity knowledge,18,19 it is thus crucial to reduce biases in ecological research, particularly in regions projected to face the most pronounced environmental changes. We integrate ecological community metadata of 7,694 sampling sites for multiple organism groups in a machine learning model framework to map the research probability across the Brazilian Amazonia, while identifying the region's vulnerability to environmental change. 15%–18% of the most neglected areas in ecological research are expected to experience severe climate or land use changes by 2050. This means that unless we take immediate action, we will not be able to establish their current status, much less monitor how it is changing and what is being lost

Pervasive gaps in Amazonian ecological research

Biodiversity loss is one of the main challenges of our time,1,2 and attempts to address it require a clear understanding of how ecological communities respond to environmental change across time and space.3,4 While the increasing availability of global databases on ecological communities has advanced our knowledge of biodiversity sensitivity to environmental changes,5,6,7 vast areas of the tropics remain understudied.8,9,10,11 In the American tropics, Amazonia stands out as the world's most diverse rainforest and the primary source of Neotropical biodiversity,12 but it remains among the least known forests in America and is often underrepresented in biodiversity databases.13,14,15 To worsen this situation, human-induced modifications16,17 may eliminate pieces of the Amazon's biodiversity puzzle before we can use them to understand how ecological communities are responding. To increase generalization and applicability of biodiversity knowledge,18,19 it is thus crucial to reduce biases in ecological research, particularly in regions projected to face the most pronounced environmental changes. We integrate ecological community metadata of 7,694 sampling sites for multiple organism groups in a machine learning model framework to map the research probability across the Brazilian Amazonia, while identifying the region's vulnerability to environmental change. 15%–18% of the most neglected areas in ecological research are expected to experience severe climate or land use changes by 2050. This means that unless we take immediate action, we will not be able to establish their current status, much less monitor how it is changing and what is being lost

Pervasive gaps in Amazonian ecological research

Biodiversity loss is one of the main challenges of our time, and attempts to address it require a clear understanding of how ecological communities respond to environmental change across time and space. While the increasing availability of global databases on ecological communities has advanced our knowledge of biodiversity sensitivity to environmental changes, vast areas of the tropics remain understudied. In the American tropics, Amazonia stands out as the world's most diverse rainforest and the primary source of Neotropical biodiversity, but it remains among the least known forests in America and is often underrepresented in biodiversity databases. To worsen this situation, human-induced modifications may eliminate pieces of the Amazon's biodiversity puzzle before we can use them to understand how ecological communities are responding. To increase generalization and applicability of biodiversity knowledge, it is thus crucial to reduce biases in ecological research, particularly in regions projected to face the most pronounced environmental changes. We integrate ecological community metadata of 7,694 sampling sites for multiple organism groups in a machine learning model framework to map the research probability across the Brazilian Amazonia, while identifying the region's vulnerability to environmental change. 15%–18% of the most neglected areas in ecological research are expected to experience severe climate or land use changes by 2050. This means that unless we take immediate action, we will not be able to establish their current status, much less monitor how it is changing and what is being lost