Throughout the course of this thesis, we give an introduction to optimal control theory and its necessary conditions, prove Pontryagin's Maximum Principle, and present the life-cycle saving under uncertain lifetime optimal control problem. We present a very involved sensitivity analysis that determines how a change in the initial wealth, discount factor, or relative risk aversion coefficient may affect the model the terminal depletion of wealth time, optimal consumption path, and optimal accumulation of wealth path. Through simulation of the life-cycle saving under uncertain lifetime model, we are not only able to present the model dynamics through time, but also to demonstrate the feasibility of the model.

L'objectif central de cette thèse est d'étudier le comportement de fraude fiscale des contribuables quand ils ne déclarent qu'une partie de leur revenu. Le premier chapitre complète la littérature existante en étudiant le niveau de déclaration du revenu et les effets de changements des taux de taxe, de pénalité et de probabilité de contrôle, en considérant des fonctions d'imposition et de pénalité non linéaire, dans le cadre de la théorie de l'espérance de l'utilité.Le cadre fourni par la théorie des perspectives cumulatives est ensuite utilisé dans le second chapitre. L'accent est mis sur la dépendance des décisions du contribuable vis-à-vis du revenu de référence introduit par cette théorie. Le troisième chapitre caractérise le barème optimal d'imposition du revenu et la stratégie de contrôle et de pénalité que doit mettre en place l'État quand le comportement de fraude des contribuables vérifie les propriétés de la théorie des perspectives. / This dissertation analyzes the tax evasion behavior of taxpayers when they do not declare their entire income. The first chapter studies the declaration of the taxpayer and the effects of changes in the tax rate, the penalty rate and the probability of audit. The tax and the penalty functions are assumed to be non linear. The setting is provided by expected utility theory. The setting provided by cumulative prospect theory is used in the second chapter. Reference dependence, which is a central point in this theory, is particularly studied. The third chapter characterizes the optimal income tax and audit schemes under taxe evasion behavior, when of tax payers behave as predicted by prospect theory.

of the master thesis Title: Modeling of risk aversion Author: František Navrátil Department: Department of Probability and Mathematical Statistics Supervisor: Doc. RNDr. Petr Lachout, CSc. Abstract: The thesis discusses various theories that are able to model investor's subjective attitude to risk. The goal of the thesis is to clearly recapitulate possible mathematical approaches and to apply them in a real situation. One of the ways to tackle the problem is to use expected utility theory and a specific shape of a utility function. Another way is to choose a suitable risk measure. Especially useful for the modelling of risk aversion is the class of spectral risk measures that enables investor to choose a risk spectrum that meets his perception of risk. The thesis contains basic definitions concerning stochastic programming - a theory essential to solve the related optimization problems. Keywords: Risk aversion, utility function, probability constraint.

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Present work describes two ways of application of psychological findings to economic theory of advertisement. Psychological findings may help with evaluation of different economic approaches of the study of advertisement. Evidence from psychology of persuasion is applied to the question, whether advertisement is used as a source of information. The work then inquires into the possibility, that advertisement can enhance utility. Summarized studies indicate, that it may indeed be so. During the inquiry, neuroeconomics is applied and it's basic methods are presented. The concluding part describes ramifications of chosen approach.

[pt] As impactantes transformações pelas quais o Brasil passou durante o início da década de 1990 exigiram mudanças profundas no setor elétrico. O Decreto n 5.163/2004 introduziu ao mercado brasileiro de energia elétrica o Ambiente de Contratação Livre (ACL), onde os agentes passaram a poder negociar livremente contratos bilaterais de compra e venda de energia. No Brasil, os agentes participantes estão expostos às bruscas variações do preço da energia no curto prazo, chamado de Preço de Liquidação das Diferenças – PLD. Devido às restrições existentes na malha de transmissão, os valores do PLD se distinguem entre os quatro Submercados existentes: Norte, Nordeste, Sul e Sudeste/Centro- Oeste. Ao fechar contratos em Submercados diferentes, o gerador deve vender a energia ao PLD local e comprá-la ao preço spot do Submercado de destino. Desta forma, o vendedor corre o risco de vender a um PLD mais baixo do que deverá comprar. O swap de submercado pode ser utilizado para anular esta exposição, mas cabe investigar o preço que cada parte deve estar disposta a pagar para fechar o negócio. Assim, é proposta uma abordagem pela Teoria da Utilidade para se chegar a estes valores. Dado que os Submercados Sudeste/Centro-Oeste e Nordeste atualmente transacionam entre si a maior carga, estes foram selecionados para avaliação. O ano de 2015 foi utilizado para delimitar o estudo. Presume-se que ambas as partes são avessas ao risco de forma decrescente e que há equilíbrio de forças na negociação. O valor final do contrato é estimado em 10,66 reais/MWh. / [en] The impacting transformations suffered by Brazil during the 1990s demanded profound changes in the eletrical sector.Decree 5.163/2004 established the Ambiente de ContrataçãoLivre (ACL), allowing participants to freely negotiate bilateral energy contracts. In Brazil, those who do so are exposed to extreme variations in spot prices, called Preço de Liquidação das Diferenças – PLD. Due to transmission capacity restrictions, PLD prices vary between the four existing submarkets: North, Northeast, South, and Southeast/Central-West. Dealing in different submarkets requires electricity generators to sell energy for local PLD and buy it for the spot price of the destination submarket. By doing so the seller may end up selling energy for a lower PLD than the buying price. Submarket swaps can be used for hedging, but what each party should be willing to pay requires investigation. Thus, to discover these prices, the Utility Theory is applied. Given that submarkets Southeast/Central-West and Northeast are currently the ones concentrating the greatest amount of transactions, these were selected for evaluation. Year 2015 was used to delimit the study. It is assumed that both parties are risk averse in a decreasing manner and that there is an equilibrium of forces in the negotiation. The final value of the contract is estimated at 10,66 reais/MWh.

Este trabalho parte da constatação de que, na história de Mato Grosso do Sul, sempre esteve presente a disputa, tão frequente no Brasil, entre os projetos de desenvolvimento de longo prazo e os interesses imediatistas do núcleo governante. Esta análise é conduzida nesta tese pelos os conceitos estruturais de desenvolvimento e subdesenvolvimento, dentro de um quadro teórico preciso, à luz das teorias macro-econômicas de Celso Furtado. Em seguida, o trabalho analisa como, em Mato Grosso do Sul, apesar da presença frequente do discurso do desenvolvimento, a força do imediatismo das elites suplantou as articulações que visassem um projeto de desenvolvimento sustentado e duradouro, capaz de melhorar as condições materiais e intelectuais da sociedade. Em particular no setor energético, que é o foco central desta tese, a contradição é marcante, principalmente em razão de que, sob vários aspectos, Mato Grosso do Sul abriga um dos mais importantes parques hidrelétricos do Brasil, sobretudo no Rio Paraná, compartilhado com São Paulo. Foi justamente a debilidade da visão de longo prazo que levou a que a implantação desse parque energético ocorresse à margem de seus governos. / This work starts from the observation that in the history of Mato Grosso do Sul, the race was always present, so frequent in Brazil, among the development projects of long term and immediate interests of the core ruling. This analysis is conducted in this thesis by the structural concepts of development and underdevelopment, within a precise theoretical framework, under Celso Furtados macroeconomic theories. Then, in work examines how, in Mato Grosso do Sul, despite the frequent presence of the development discourse, the strength of the immediacy of the elites supplanted the joints which are aimed at a project of sustainable development and durable, capable of improving the material conditions and intellectual society. Particularly in the energy sector that is the focus of this thesis, the contradiction is striking, especially considering that in many ways Mato Grosso do Sul is home to one of the most important hydroelectric parks in Brazil, especially in the Paraná River, shared with the state of São Paulo. It was precisely the weakness of long term vision that led to the deployment of such energy park occurred outside of their governments.

Este trabalho tem por finalidade o estudo teórico e experimental de avaliação da degradação em postes de madeira utilizados em redes de energia elétrica. Com base em ampla revisão bibliográfica, de dados climáticos de várias cidades do Estado de São Paulo e resultados de ensaios de perfuração controlada realizadas em campo, em vários municípios do Estado de São Paulo, apresenta um modelo de apodrecimento de madeira em contato com o solo, identificando quais as cidades são mais e menos agressivas à madeira nestas condições, propondo a simplificação deste modelo, facilitando sua utilização na previsão da vida útil de madeiras em contato com o solo, predizendo o grau de deterioração destes. O modelo proposto se mostrou bastante adequado, dando uma boa previsão da deterioração de postes nas diversas regiões do Estado. / The purpose of this paper is the theoretical and experimental study of evaluation of timber deterioration in used poles in nets of electric energy. Basing on ample bibliographical reviews of climatic data of some cities in the State of São Paulo and results of controlled perforation testing done in field, in some cities of the State of São Paulo, it presents a model of timber decay in contact with the ground, identifying which cities are more aggressive or less aggressive to the wood in these conditions, proposing the simplification of this model, facilitating its use in the forecast of the timber service life in contact with the ground, predicting the degree of deterioration in them. The proposed model proved to be sufficiently adequate giving a good forecast of the pole deterioration in several regions of the State.

Testam-se quatro utilidades com o formato S das curvas de saturação - gama, logística, Cauchy e Cauchy modificada - no modelo básico de apreçamento de ativos de Lucas, com séries temporais do mercado americano. Estabelecendo-se um parâmetro que acompanha o nível de consumo per capita , constata-se que todas resolvem o chamado riskfree puzzle. A gama e a Cauchy modificada saem-se melhor no apreçamento dos 25 ativos do portfolio de Fama e French e esta última é eleita a vencedora, pelas suas propriedades assintóticas e por apresentar coeficiente médio (no sentido cross-section) de aversão relativa ao risco na faixa considerada normal (entre 0 e 5). A Cauchy modificada regulariza a utilidade de Constantinides-Cochrane-Campbel, de formação de hábito, permitindo que o trecho abaixo do consumo habitual seja usado, com isso dispensando o uso de truques para impedir que o consumo suavizado ultrapasse o real. Constatou-se a manutenção daquele coeficiente médio dentro da faixa normal, em um nível pouco abaixo do americano, no caso do mercado brasileiro. Nesse sentido de média crosssection, poderia-se dizer que a utilidade aqui proposta resolve o chamado equity premium puzzle. / Four S-shaped utility functions are tested - gamma, logistic, Cauchy and modified Cauchy - on Lucas asset pricing model with American market time series. Establishing a parameter that follows the level of the per capita consumption, it is shown that all of them solve the so called risk free puzzle. The gamma utility and the modified Cauchy are the ones with better pricing power with respect to Fama and French\'s 25 book-to-market portfolio and the last one is elected the winner, for its asymptotic properties and for exhibiting mean (in the cross-section sense) relative risk aversion coefficient inside the accepted normal range (between 0 and 5). The modified Cauchy utility regularizes the habit-formation Constantinides-Cochrane-Campbel utility function, allowing the usage of the stretch below the habit consumption level, thus doing without the need of tricks to forbid the smoothed consumption series from outgrowing the real one. In the Brazilian market, the mean relative risk aversion coefficient also remains inside the acceptable region, on a slightly lower level. In this mean cross-section sense, it might be possible to state that the utility here proposed solves the equity premium puzzle.

<p>People living in developing countries or undeveloped regions often do not have proper access to quantities of safe, clean water to fulfill their daily needs. Certain members of the families, often women and children, walk miles every day to collect surface waters that are frequently contaminated. To improve water availability and quality, a sustainable mechanical solution to more safely access groundwater has been developed.</p> <p> </p> <p>A well-driving attachment for a PUP (Purdue Utility Project) vehicle provides a low-cost means for installing driven type wells in areas of high to medium water table heights. PUP vehicles have a niche in developing countries, as they offer impressive value and utility in comparison to other powered machines. The vehicles are built and sourced using locally available materials with basic tooling. A hydraulic post driver has been attached to the rear of a PUP frame to serve as an impact mechanism, driving a well point and a series of inter-connecting pipes to serve as a permanent casing for the well. </p> <p> </p> <p>Water wells were tested at four different test sites around central Indiana, with the deepest well reaching 23 feet. This suggests that the Well-Driver PUP can install driven water wells in areas of medium to high water tables and may be suitable for a development setting. Water wells can be installed on a communal basis, thus providing an increased level of hygiene and standards of living. Low-cost driven water wells will provide a drinking water supply that is better protected than a hand-dug well and will reduce the likelihood of disease caused by waterborne pathogens. Development of the Well-Driver PUP prototype and its applications will be discussed.</p>