Evolutionary finance studies financial markets from an evolutionary point of view. A financial market can be interpreted in the context of its evolution: it can be understood as a dynamical system in which frequently interacting investment strategies compete for market capital. We are mainly interested in the long-run performance of investment strategies. This thesis explores the "Darwinian theory" of portfolio selection. An asset market can be modelled by a game-theoretic evolutionary model in which asset prices are endogenously determined by market clearing condition. A general version of the Kelly rule is shown to allow an investor to "survive" in the asset market. We then investigate the stochastic model with independent and identical distributed states of the world from a different, game-theoretic, angle and examine Nash equilibrium strategies, satisfying equilibrium conditions with probability one. Evolutionary finance and asset market games also provide new angles to present fundamental facts of capital growth theory. Relations between financial growth and the property of "survival" of investment strategies are established in the market selection process.

We study evolutionary models of financial markets. In particular, we study an evolutionary market model with short-lived assets and an evolutionary model with long-lived assets. In the long-lived asset market, investors are allowed to use general dynamic investment strategies. We find sufficient conditions for the Kelly portfolio rule to dominate the market exponentially fast. Moreover, when investors use simple strategies but have incorrect beliefs, we show that the strategy which is "closer" to the Kelly rule cannot be driven out of the market. This means that this strategy will either dominate or at least survive, i.e., the relative market share does not converge to zero. In the market with short-lived assets, we study the dynamics when the states of the world are not identically distributed. This marks the first attempt to study the dynamics of the market when the probability of success changes according to the relative shares of investors. In this problem, we first study a skew product of the random dynamical system associates with the market dynamics. In particular, we compute the Lyapunov exponents of the skew product. This enables us to produce a "surviving" investment strategy, i.e., the investor who follows this rule will dominate the market or at least survive. All the mathematical tools in the thesis lie within the framework of random dynamical systems.

Thema der Dissertation ist zum einen die Quantifizierung und zum anderen die endogene Modellierung von Finanzrisiken. Die mathematische Analyse führt unter anderem auf Zusammenhänge finanzmathematischer Probleme mit der Theorie großer Abweichungen, der Choquet-Theorie, der Theorie interagierender Teilchensysteme und der Theorie dynamischer Systeme. Die ersten zwei Kapitel der Arbeit beleuchten die Bemessung von Finanzrisiken aus zwei unterschiedlichen Perspektiven. In Kapitel 1 analysieren wir die Berechnung von Risikomaßen mittels Monte Carlo Methoden. In Kapitel 2 wird die Rolle von Information und Zeit bei der Bewertung von Finanzrisiken untersucht. Die Modellierung von Finanzrisiken auf Märkten interagierender Akteure wird in den beiden letzten Kapiteln der Arbeit in zwei Fallstudien betrachtet. In der ersten Fallstudie in Kapitel 3 befassen wir uns dabei mit dem Zusammenhang von Kreditrisiken und Ansteckungsprozessen von Firmen, die mit ihren Geschäftspartnern interagieren. In der zweiten Fallstudie in Kapitel 4 beleuchten wir die Marktinteraktion von eingeschränkt rationalen Investoren in einem evolutionären Marktselektionsmodell. / In this thesis, we study monetary measures and endogenous models of financial risk. The mathematical analysis identifies connections between problems in mathematical finance on the one hand and large deviations, Choquet-theory, interacting particle systems, and dynamical systems on the other hand. The first part of the thesis considers two aspects of the quantification of financial risk. In the first chapter, we focus on the calculation of risk measurements by Monte Carlo simulation. In the second chapter, we investigate a particular class of dynamic risk measures. In the second part we analyze two models of financial risk in economies with interacting agents. First, we focus in the third chapter on credit contagion of firms which interact with each other in a network of business partners. Second, we investigate in the fourth chapter the market interaction of investors with bounded rationality in an evolutionary selection market model.

Um dos temas mais discutidos na área de finanças é a forma como os mercados se estruturam sob perspectiva informacional, precificando ativos financeiros. Uma das teorias centrais de discussão é a Hipótese de Eficiência dos Mercados (HEM) de Eugene Fama (1970), derivada da teoria de utilidade. Um dos pontos centrais de discussão e critica da HEM são seus pressupostos quanto à modelagem do comportamento humano, totalmente racional e oportunista. Uma segunda linha de estudos apresenta um contraponto a esse modelo de ser humano utilizado nas teorias neoclássicas de finanças, utilizando um modelo de agente que possui falhas no processo de tomada de decisão financeira em função de uma racionalidade limitada e de vieses cognitivos, que impactam sobre o preço dos ativos negociados (Tversky & Kahneman, 1979; Thaler, 1985). A Hipótese de Mercados Adaptativos (HMA), de Andrew Lo (2004, 2005), é uma das teorias que conciliam a estrutura neoclássica da HEM com o comportamento não ótimo do agente, considerando novas estruturas de tomada de decisão financeira pelo investidor, como aprendizado, adaptação e vieses comportamentais, apresentando dinâmicas de mercado semelhantes a características biológicas, com impactos do ambiente e seleção natural como direcionadores da eficiência dos mercados. Desta forma, esse trabalho tem como objetivo verificar se existe aderência do conceito de evolução e do impacto do ambiente macroeconômico sobre a eficiência informacional dos mercados financeiros, verificando a capacidade de adaptação do mercado a mudanças do ambiente, e quais fatores apresentam maior grau de explicação no processo de adaptação e eficiência dos mercados em diferentes países. Para isso foram analisados os índices de preços e retornos de 48 economias, assim como informações econômico-institucionais sobre os países aos quais estavam relacionados, por meio do desenvolvimento de uma métrica de ineficiência informacional relativa dos mercados e posterior análise por meio de modelos descritivos e multinível. Foi identificado que há comportamentos cíclicos de eficiência ao longo do tempo, e os graus de eficiência diferem-se entre as economias estudadas, assim como há evidências de que há variação do comportamento de eficiência quando da mudança do cenário econômico. Adicionalmente foi identificado que características ambientais (como instituições e comportamento geral da economia) também apresentam efeitos sobre o grau de ineficiência relativa de mercados, e sua relação está associada ao comportamento previsto na HMA. / One of the most discussed topics in finance research is the way of markets are structured from an informational perspective, pricing financial assets. One of the central theories of discussion is Eugene Fama\'s Market Efficiency Hypothesis (HEM) (1970), derived from utility theory. One of the central points of discussion and critics of HEM is its assumptions about the modeling of human behavior, totally rational and opportunistic. The second line of studies shows a counterpoint to this model of human behavior used in neoclassical finance theories, by an agent model that has flaws in financial decision-making process due to a bounded rationality and cognitive biases impacting on the price of the traded assets (Tversky & Kahneman, 1979; Thaler, 1985). The Andrew Lo\'s (2004, 2005) Adaptive Market Hypothesis (HMA) is one of the theories that reconcile the neoclassical structure of HEM with the agent\'s non-optimal behavior, considering new structures of financial decision-making by the investor, such as learning, adaptation and behavioral biases, presenting market dynamics like biological characteristics with environmental impacts and natural selection as drivers of market efficiency. In this way, the objective of this work is to verify if there is adherence to the concept of evolution and the impact of the macroeconomic environment on the informational efficiency of the financial markets, observing the adaptability of the market to changes in the environment, and which factors present a greater degree of explanation in the process of adaptation and efficiency of markets in different countries. To do so, we analyzed the price and return indices of 48 economies, as well as economic-institutional information about the related countries, through the development of a metric of relative informational inefficiency and subsequent analysis through descriptive and multilevel models. It has been identified that there are cyclical efficiency behaviors over time, and the efficiency levels differ between the studied economies, and evidence about the changes in the efficiency behavior when the economic scenario changes. Additionally, it was identified that environmental characteristics (such as institutions and general economic behavior) also have effects on the degree of relative market inefficiency, and their relation is associated with the behavior predicted in the HMA

Um dos temas mais discutidos na área de finanças é a forma como os mercados se estruturam sob perspectiva informacional, precificando ativos financeiros. Uma das teorias centrais de discussão é a Hipótese de Eficiência dos Mercados (HEM) de Eugene Fama (1970), derivada da teoria de utilidade. Um dos pontos centrais de discussão e critica da HEM são seus pressupostos quanto à modelagem do comportamento humano, totalmente racional e oportunista. Uma segunda linha de estudos apresenta um contraponto a esse modelo de ser humano utilizado nas teorias neoclássicas de finanças, utilizando um modelo de agente que possui falhas no processo de tomada de decisão financeira em função de uma racionalidade limitada e de vieses cognitivos, que impactam sobre o preço dos ativos negociados (Tversky & Kahneman, 1979; Thaler, 1985). A Hipótese de Mercados Adaptativos (HMA), de Andrew Lo (2004, 2005), é uma das teorias que conciliam a estrutura neoclássica da HEM com o comportamento não ótimo do agente, considerando novas estruturas de tomada de decisão financeira pelo investidor, como aprendizado, adaptação e vieses comportamentais, apresentando dinâmicas de mercado semelhantes a características biológicas, com impactos do ambiente e seleção natural como direcionadores da eficiência dos mercados. Desta forma, esse trabalho tem como objetivo verificar se existe aderência do conceito de evolução e do impacto do ambiente macroeconômico sobre a eficiência informacional dos mercados financeiros, verificando a capacidade de adaptação do mercado a mudanças do ambiente, e quais fatores apresentam maior grau de explicação no processo de adaptação e eficiência dos mercados em diferentes países. Para isso foram analisados os índices de preços e retornos de 48 economias, assim como informações econômico-institucionais sobre os países aos quais estavam relacionados, por meio do desenvolvimento de uma métrica de ineficiência informacional relativa dos mercados e posterior análise por meio de modelos descritivos e multinível. Foi identificado que há comportamentos cíclicos de eficiência ao longo do tempo, e os graus de eficiência diferem-se entre as economias estudadas, assim como há evidências de que há variação do comportamento de eficiência quando da mudança do cenário econômico. Adicionalmente foi identificado que características ambientais (como instituições e comportamento geral da economia) também apresentam efeitos sobre o grau de ineficiência relativa de mercados, e sua relação está associada ao comportamento previsto na HMA. / One of the most discussed topics in finance research is the way of markets are structured from an informational perspective, pricing financial assets. One of the central theories of discussion is Eugene Fama\'s Market Efficiency Hypothesis (HEM) (1970), derived from utility theory. One of the central points of discussion and critics of HEM is its assumptions about the modeling of human behavior, totally rational and opportunistic. The second line of studies shows a counterpoint to this model of human behavior used in neoclassical finance theories, by an agent model that has flaws in financial decision-making process due to a bounded rationality and cognitive biases impacting on the price of the traded assets (Tversky & Kahneman, 1979; Thaler, 1985). The Andrew Lo\'s (2004, 2005) Adaptive Market Hypothesis (HMA) is one of the theories that reconcile the neoclassical structure of HEM with the agent\'s non-optimal behavior, considering new structures of financial decision-making by the investor, such as learning, adaptation and behavioral biases, presenting market dynamics like biological characteristics with environmental impacts and natural selection as drivers of market efficiency. In this way, the objective of this work is to verify if there is adherence to the concept of evolution and the impact of the macroeconomic environment on the informational efficiency of the financial markets, observing the adaptability of the market to changes in the environment, and which factors present a greater degree of explanation in the process of adaptation and efficiency of markets in different countries. To do so, we analyzed the price and return indices of 48 economies, as well as economic-institutional information about the related countries, through the development of a metric of relative informational inefficiency and subsequent analysis through descriptive and multilevel models. It has been identified that there are cyclical efficiency behaviors over time, and the efficiency levels differ between the studied economies, and evidence about the changes in the efficiency behavior when the economic scenario changes. Additionally, it was identified that environmental characteristics (such as institutions and general economic behavior) also have effects on the degree of relative market inefficiency, and their relation is associated with the behavior predicted in the HMA