Com a crescente demanda de modelagem de riscos dependentes, enfatizamos neste trabalho a teoria de cópulas e algumas medidas de dependência tais como coeficiente de correlação linear, coeficiente de correlação de Spearman. Mostramos algumas interpretações errôneas sobre o coeficiente de correlação linear e como podemos realizar simulações de variáveis aleatórias com determinadas marginais e dependência. Realizamos uma aplicação na área de seguros para determinar o capital alocado da seguradora. / With the growing demand for modeling dependent risk, in this study we emphasize the theory of copulas and some measures of dependence such as linear correlation coefficient and Spearman correlation coefficient. We show some misleading interpretations on the linear correlation coefficient, and how we can perform simulations of random variables with some marginals and dependence. We conduct an application in the insurance area to determine the allocated capital of the insurer.

O modelo de comercialização de energia elétrica operante no Brasil é fruto da reestruturação do Setor Elétrico Brasileiro (SEB), que se iniciou na década de 90. Este modelo atual, mais estruturado, impulsionou os investimentos privados no setor nos últimos anos, fazendo com que a comercialização de energia se tornasse algo de grande representatividade dentro do setor elétrico. Este modelo de comercialização como é hoje, dividido em dois ambientes, dinâmico e em constante evolução, é alvo de inúmeros investidores, principalmente no Ambiente de Contratação Livre (ACL) onde o número de agentes cresceu consideravelmente nos últimos anos, e gerou movimentações financeiras recordes. Associado a este crescimento expressivo, os riscos inerentes de mercado também se mostram relevantes e de fundamental necessidade de gerenciamento para o equilíbrio financeiro do investidor. Dessa forma, este trabalho propõe uma análise acerca da comercialização de energia no mercado brasileiro, quanto ao gerenciamento do risco por parte de um agente gerador operando no ACL, através da implementação de um otimizador contratual que ajude na tomada de decisão de quanta energia destinar a cada contrato, de modo a maximizar a receita do agente a um risco controlável. / The present marketing model of electric power in Brazil is the result of the restructuring of the Brazilian Electric Sector (BES), which began in the 90s. This current model, somewhat more structured, stimulated private investment in the sector in recent years; this way the electric power´s market acquired substantial representation within the electricity sector. The current market model, having two different commercial environments, dynamic and constantly evolving, has been attracting many investors, especially in the Free Contracting Environment (FCE) where the number of agents has grown considerably in recent years, and generated record number of financial transactions. Associated with this significant growth, the inherent risks in this market are effectively of concern and need being managed to ensure the financial balance of the investor. Therefore, this work proposes an analysis about the energy trading in the Brazilian market, as to the management of risk by an agent generator operating in the FCE, through the implementation of a contract optimizer that helps in making decisions on how construct a contract portfolio in order to maximizes the agent revenue under a controllable risk.

O planejamento da operação energética do sistema interligado nacional brasileiro é realizado por uma cadeia de modelos computacionais de otimização e simulação da operação. Entretanto, o risco de déficit, um importante indicador de segurança energética no setor elétrico, é tratado como uma variável de saída dos modelos computacionais. No planejamento de médio prazo é utilizado o software NEWAVE, que utiliza uma representação agregada em subsistemas equivalentes. Este trabalho propõe a implementação de um modelo de otimização linear para o planejamento da operação de médio prazo capaz de considerar o risco de déficit em sua formulação. Para o controle de risco de déficit, é proposta a utilização da métrica de risco conhecida por CVaR (Conditional Value at Risk), por se caracterizar como uma métrica de risco coerente, além de poder ser implementada por meio de um conjunto de restrições lineares. / The energetic operation planning of the Brazilian interconnected system is performed by a chain of computational models for the system optimization and simulation. However, the deficit risk, an important energy security indicator for the electric sector, is treated as an output variable on the computational models. In the medium-term of the energetic planning is used the software NEWAVE, which uses equivalent systems on aggregated representation. This work proposes the implementation of a linear optimization model for the medium-term of the energetic planning able to consider the deficit risk in its own formulation. To control the deficit risk is proposed the use of the risk metric known as CVaR (Conditional Value at Risk), because it is characterized as a coherent risk metric, and can be implemented through a set of linear constraints.

O planejamento da operação energética do sistema interligado nacional brasileiro é realizado por uma cadeia de modelos computacionais de otimização e simulação da operação. Entretanto, o risco de déficit, um importante indicador de segurança energética no setor elétrico, é tratado como uma variável de saída dos modelos computacionais. No planejamento de médio prazo é utilizado o software NEWAVE, que utiliza uma representação agregada em subsistemas equivalentes. Este trabalho propõe a implementação de um modelo de otimização linear para o planejamento da operação de médio prazo capaz de considerar o risco de déficit em sua formulação. Para o controle de risco de déficit, é proposta a utilização da métrica de risco conhecida por CVaR (Conditional Value at Risk), por se caracterizar como uma métrica de risco coerente, além de poder ser implementada por meio de um conjunto de restrições lineares. / The energetic operation planning of the Brazilian interconnected system is performed by a chain of computational models for the system optimization and simulation. However, the deficit risk, an important energy security indicator for the electric sector, is treated as an output variable on the computational models. In the medium-term of the energetic planning is used the software NEWAVE, which uses equivalent systems on aggregated representation. This work proposes the implementation of a linear optimization model for the medium-term of the energetic planning able to consider the deficit risk in its own formulation. To control the deficit risk is proposed the use of the risk metric known as CVaR (Conditional Value at Risk), because it is characterized as a coherent risk metric, and can be implemented through a set of linear constraints.

O modelo de comercialização de energia elétrica operante no Brasil é fruto da reestruturação do Setor Elétrico Brasileiro (SEB), que se iniciou na década de 90. Este modelo atual, mais estruturado, impulsionou os investimentos privados no setor nos últimos anos, fazendo com que a comercialização de energia se tornasse algo de grande representatividade dentro do setor elétrico. Este modelo de comercialização como é hoje, dividido em dois ambientes, dinâmico e em constante evolução, é alvo de inúmeros investidores, principalmente no Ambiente de Contratação Livre (ACL) onde o número de agentes cresceu consideravelmente nos últimos anos, e gerou movimentações financeiras recordes. Associado a este crescimento expressivo, os riscos inerentes de mercado também se mostram relevantes e de fundamental necessidade de gerenciamento para o equilíbrio financeiro do investidor. Dessa forma, este trabalho propõe uma análise acerca da comercialização de energia no mercado brasileiro, quanto ao gerenciamento do risco por parte de um agente gerador operando no ACL, através da implementação de um otimizador contratual que ajude na tomada de decisão de quanta energia destinar a cada contrato, de modo a maximizar a receita do agente a um risco controlável. / The present marketing model of electric power in Brazil is the result of the restructuring of the Brazilian Electric Sector (BES), which began in the 90s. This current model, somewhat more structured, stimulated private investment in the sector in recent years; this way the electric power´s market acquired substantial representation within the electricity sector. The current market model, having two different commercial environments, dynamic and constantly evolving, has been attracting many investors, especially in the Free Contracting Environment (FCE) where the number of agents has grown considerably in recent years, and generated record number of financial transactions. Associated with this significant growth, the inherent risks in this market are effectively of concern and need being managed to ensure the financial balance of the investor. Therefore, this work proposes an analysis about the energy trading in the Brazilian market, as to the management of risk by an agent generator operating in the FCE, through the implementation of a contract optimizer that helps in making decisions on how construct a contract portfolio in order to maximizes the agent revenue under a controllable risk.

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Teachers need interventions to improve at-risk students' self-efficacy, which may improve their academic performance in school. The purpose of this qualitative case study was to explore the perceptions of elementary school teachers at a Texas public middle school as to what research-based interventions they felt would improve the self-efficacy of these students. Bandura's social cognitive theory, which framed the study, indicates that self-efficacy beliefs affect the courses of action that people seek and the choices people make. Many at-risk students who experience a lack of academic success have low self-efficacy, which may affect their school performance. The research questions that guided the study focused on teachers' perceptions of whether a school-based mentoring program, counseling services, or an afterschool program would best help at-risk students improve their self-efficacy. Semi-structured interviews were conducted to collect data from 6 teacher participants who were purposely selected from different grade levels at the school. The data were transcribed and analyzed using hand-coding procedures to determine categories and themes from the transcripts. The findings revealed that teachers thought that a school-based mentoring program would have the most positive impact in improving the self-efficacy of at-risk students. The results prompted the development of a training program for mentors. Positive social change may result when at-risk students benefit from mentors who are properly trained on ways to meaningfully impact them.

Cette thèse est consacrée à des problématiques numériques probabilistes liées à la modélisation, au contrôle et à la gestion du risque et motivées par des applications dans les marchés de l'énergie. Le principal outil utilisé est la théorie des algorithmes stochastiques et des méthodes de simulation. Cette thèse se compose de trois parties. La première est dévouée à l'estimation de deux mesures de risque de la distribution L des pertes d'un portefeuille: la Value-at-Risk (VaR) et la Conditional Value-at-Risk (CVaR). Cette estimation est effectuée à l'aide d'un algorithme stochastique combiné avec une méthode de réduction de variance adaptative. La première partie de ce chapitre traite du cas de la dimension finie, la deuxième étend la première au cas d'une fonction de la trajectoire d'un processus et la dernière traite du cas des suites à discrépance faible. Le deuxième chapitre est dédié à des méthodes de couverture du risque en CVaR dans un marché incomplet opérant à temps discret à l'aide d'algorithmes stochastiques et de quantification vectorielle optimale. Des résultats théoriques sur la couverture en CVaR sont présentés puis les aspects numériques sont abordés dans un cadre markovien. La dernière partie est consacrée à la modélisation conjointe des prix des contrats spot Gaz et l'Electricité. Le modèle multi-facteur présenté repose sur des processus d'Ornstein stationnaires à coefficient de diffusion paramétrique.

Mit der hier vorliegenden Arbeit wird ein mikroökonomisches Multiagentenmodell eines Produktionssektors vorgeschlagen. Das Modell folgt einem post-walrasianischem Ungleichgewichtsansatz und beschreibt optimierende Agenten der Produktionsseite. Diese berücksichtigen in probabilistischen Nebenbedingungen Risiken des Cash Flow, die sich aus unsicheren Absatzmengen ergeben. Produzenten stehen in monopolistischer Konkurrenz und lernen durch Beobachten. Wird vorliegendes Modell in ein Totalmodell integriert, so wird es möglich, die sich aus der Klimadebatte ergebenden, notwendigen Veränderungen im Investitions- und Produktionsverhalten zu diskutieren und darzustellen. / In the following thesis I propose a microeconomic Multi-Agent-Model of a production sector. I apply a Post-Walrasian disequilibrium approach and describe optimizing agents. These agents use chance constraints which depict a Cash Flow at Risk approach. Agents act in a Monopolistic-Competition environment.

Within our research group Bayesian Risk Solutions we have coined the idea of a Bayesian Risk Management (BRM). It claims (1) a more transparent and diligent data analysis as well as (2)an open-minded incorporation of human expertise in risk management. In this dissertation we formulize a framework for BRM based on the two pillars Hardcore-Bayesianism (HCB) and Softcore-Bayesianism (SCB) providing solutions for the claims above. For data analysis we favor Bayesian statistics with its Markov Chain Monte Carlo (MCMC) simulation algorithm. It provides a full illustration of data-induced uncertainty beyond classical point-estimates. We calibrate twelve different stochastic processes to four years of CO2 price data. Besides, we calculate derived risk measures (ex ante/ post value-at-risks, capital charges, option prices) and compare them to their classical counterparts. When statistics fails because of a lack of reliable data we propose our integrated Bayesian Risk Analysis (iBRA) concept. It is a basic guideline for an expertise-driven quantification of critical risks. We additionally review elicitation techniques and tools supporting experts to express their uncertainty. Unfortunately, Bayesian thinking is often blamed for its arbitrariness. Therefore, we introduce the idea of a Bayesian due diligence judging expert assessments according to their information content and their inter-subjectivity. / Die vorliegende Arbeit befasst sich mit den Ansätzen eines Bayes’schen Risikomanagements zur Messung von Risiken. Dabei konzentriert sich die Arbeit auf folgende zentrale Fragestellungen: (1) Wie ist es möglich, transparent Risiken zu quantifizieren, falls nur eine begrenzte Anzahl an geeigneten historischen Beobachtungen zur Datenanalyse zur Verfügung steht? (2) Wie ist es möglich, transparent Risiken zu quantifizieren, falls mangels geeigneter historischer Beobachtungen keine Datenanalyse möglich ist? (3) Inwieweit ist es möglich, Willkür und Beliebigkeit bei der Risikoquantifizierung zu begrenzen? Zur Beantwortung der ersten Frage schlägt diese Arbeit die Anwendung der Bayes’schen Statistik vor. Im Gegensatz zu klassischen Kleinste-Quadrate bzw. Maximum-Likelihood Punktschätzern können Bayes’sche A-Posteriori Verteilungen die dateninduzierte Parameter- und Modellunsicherheit explizit messen. Als Anwendungsbeispiel werden in der Arbeit zwölf verschiedene stochastische Prozesse an CO2-Preiszeitreihen mittels des effizienten Bayes’schen Markov Chain Monte Carlo (MCMC) Simulationsalgorithmus kalibriert. Da die Bayes’sche Statistik die Berechnung von Modellwahrscheinlichkeiten zur kardinalen Modellgütemessung erlaubt, konnten Log-Varianz Prozesse als mit Abstand beste Modellklasse identifiziert werden. Für ausgewählte Prozesse wurden zusätzlich die Auswirkung von Parameterunsicherheit auf abgeleitete Risikomaße (ex-ante/ ex-post Value-at-Risks, regulatorische Kapitalrücklagen, Optionspreise) untersucht. Generell sind die Unterschiede zwischen Bayes’schen und klassischen Risikomaßen umso größer, je komplexer die Modellannahmen für den CO2-Preis sind. Überdies sind Bayes’sche Value-at-Risks und Kapitalrücklagen konservativer als ihre klassischen Pendants (Risikoprämie für Parameterunsicherheit). Bezüglich der zweiten Frage ist die in dieser Arbeit vertretene Position, dass eine Risikoquantifizierung ohne (ausreichend) verlässliche Daten nur durch die Berücksichtigung von Expertenwissen erfolgen kann. Dies erfordert ein strukturiertes Vorgehen. Daher wird das integrated Bayesian Risk Analysis (iBRA) Konzept vorgestellt, welches Konzepte, Techniken und Werkzeuge zur expertenbasierten Identifizierung und Quantifizierung von Risikofaktoren und deren Abhängigkeiten vereint. Darüber hinaus bietet es Ansätze für den Umgang mit konkurrierenden Expertenmeinungen. Da gerade ressourceneffiziente Werkzeuge zur Quantifizierung von Expertenwissen von besonderem Interesse für die Praxis sind, wurden im Rahmen dieser Arbeit der Onlinemarkt PCXtrade und die Onlinebefragungsplattform PCXquest konzipiert und mehrfach erfolgreich getestet. In zwei empirischen Studien wurde zudem untersucht, inwieweit Menschen überhaupt in der Lage sind, ihre Unsicherheiten zu quantifizieren und inwieweit sie Selbsteinschätzungen von Experten bewerten. Die Ergebnisse deuten an, dass Menschen zu einer Selbstüberschätzung ihrer Prognosefähigkeiten neigen und tendenziell hohes Vertrauen in solche Experteneinschätzungen zeigen, zu denen der jeweilige Experte selbst hohes Zutrauen geäußert hat. Zu letzterer Feststellung ist jedoch zu bemerken, dass ein nicht unbeträchtlicher Teil der Befragten sehr hohe Selbsteinschätzung des Experten als negativ ansehen. Da der Bayesianismus Wahrscheinlichkeiten als Maß für die persönliche Unsicherheit propagiert, bietet er keinerlei Rahmen für die Verifizierung bzw. Falsifizierung von Einschätzungen. Dies wird mitunter mit Beliebigkeit gleichgesetzt und könnte einer der Gründe sein, dass offen praktizierter Bayesianismus in Deutschland ein Schattendasein fristet. Die vorliegende Arbeit stellt daher das Konzept des Bayesian Due Diligence zur Diskussion. Es schlägt eine kriterienbasierte Bewertung von Experteneinschätzungen vor, welche insbesondere die Intersubjektivität und den Informationsgehalt von Einschätzungen beleuchtet.