Nesta tese abordamos o problema do hedging de mínima variância de derivativos em mercados incompletos usando a teoria de controle ótimo estocástico com critério quadrático de otimização. Desenvolvemos um modelo geral de apreçamento e hedging de derivativos em mercados incompletos, a tempo discreto, que é capaz de acomodar qualquer tipo de payoff com característica européia que dependa de n ativos de risco. Nesse modelo, o mercado pode apresentar diferentes modos de operação, o que foi formalizado matematicamente por meio de uma cadeia de Markov. Também desenvolvemos um modelo geral de apreçamento e hedging de derivativos em mercados incompletos, a tempo discreto e espaço de estados contínuo, que é capaz de acomodar qualquer tipo de payoff com característica européia que dependa de um ativo de risco cujos retornos sejam representados por um processo de difusão com saltos. Desenvolvemos, ainda, expressões analíticas fechadas para o apreçamento e hedging de uma opção de compra européia vanilla em duas situações: (1) quando os retornos do ativo de risco são representados por um processo de difusão com saltos, e (2) quando os retornos do ativo de risco são representados por um processo de Wiener. Por fim, realizamos simulações numéricas para o controle (hedging) de uma opção de compra européia vanilla quando os retornos do ativo de risco são representados por um processo de Wiener, e comparamos os resultados obtidos com a estratégia de controle derivada do modelo de Black & Scholes. / In this thesis we approach the mean-variance hedging problem of derivatives in incomplete markets employing the theory of stochastic optimal control with quadratic optimization criteria. We developed a general derivatives pricing and hedging model in incomplete markets, in discrete time, capable of accommodating any type of European payoff contingent on n risky assets. In this model, the market may exhibit different operating modes, which were mathematically formalized by means of a Markov chain. We also developed a general derivatives pricing and hedging model in incomplete markets, in discrete time and continuous state space, capable of accommodating any type of European payoff contingent on one risky asset whose returns are described by a jump diffusion process. Even further, we developed closed-form analytical expressions for the pricing and hedging of a European vanilla call option in two situations: (1) when the risky asset returns are described by a jump diffusion process, and (2) when the risky asset returns are described by a Wiener process. Finally, we simulated the control (hedging) of a European vanilla call option when the risky asset returns are described by a Wiener process, and compared the results to those obtained with the control strategy derived from the Black & Scholes model.

Abordaremos a teoria do transporte otimo demonstrando o teorema da dualidade de Kantorovich para uma classe ampla de funções custo. Tal resultado desempenha um papel de suma importância na teoria do transporte otimo. Uma ferramenta importante utilizada e o teorema da dualidade de Fenchel-Rockafellar, aqui enunciado e demonstrado em bastante generalidade. Demonstramos tamb em o teorema da dualidade de Kantorovich-Rubinstein, que trata do caso particular da função custo distância. / We analyze the optimal transport theory proving the Kantorovich duality theorem for a wide class of cost functions. Such result plays an extremely important role in the optimal transport theory. An important tool used here is the Fenchel-Rockafellar duality theorem, which we state and prove in a general case. We also prove the Kantorovich-Rubinstein duality theorem, which deals with the particular case of cost function given by the distance.

Made available in DSpace on 2014-10-09T12:50:30Z (GMT). No. of bitstreams: 0 / Made available in DSpace on 2014-10-09T13:58:49Z (GMT). No. of bitstreams: 1 00045.pdf: 1150397 bytes, checksum: fd8a86947b37fabf9aa8ff7b1e99d2a9 (MD5) / Dissertacao (Mestrado) / IEA/D / Escola Politecnica, Universidade de Sao Paulo - POLI/USP

Submitted by Geandra Rodrigues (geandrar@gmail.com) on 2018-01-11T17:29:03Z No. of bitstreams: 1 exuperrybarroscosta.pdf: 14654639 bytes, checksum: f25579d82da6242e77a04745322538ad (MD5) / Approved for entry into archive by Adriana Oliveira (adriana.oliveira@ufjf.edu.br) on 2018-01-23T13:44:17Z (GMT) No. of bitstreams: 1 exuperrybarroscosta.pdf: 14654639 bytes, checksum: f25579d82da6242e77a04745322538ad (MD5) / Made available in DSpace on 2018-01-23T13:44:17Z (GMT). No. of bitstreams: 1 exuperrybarroscosta.pdf: 14654639 bytes, checksum: f25579d82da6242e77a04745322538ad (MD5) Previous issue date: 2017-09-15 / O presente trabalho propõe uma nova metodologia de Geração de Sinal Sub-Ótimo de Excitação e Estimação Ótima de Parâmetros de sistemas não lineares. É proposto que a avaliação de cada sinal deva considerar, entre outros fatores, a diferença entre os parâmetros reais da planta e os obtidos pela estimação. Entretanto esta métrica não é trivial de ser obtida uma vez que os valores reais são desconhecidos. Para tanto é adotada a hipótese de que, se um sistema real puder ser razoavelmente aproximado por uma caixa branca, é possível utilizar este modelo como referência para indicar o impacto de um sinal sobre a estimação paramétrica. Desta forma, é utilizada uma metodologia de otimização dividida em dois níveis: (i) Nível Interno; para um dado sinal de excitação um método de otimização não linear busca o conjunto ótimo de parâmetros que minimiza o erro entre os sinais de saída do modelos original e do de referência. (ii) No nível externo um método de otimização baseado em meta-heurística é responsável por encontrar o melhor sinal de excitação com base na função custo composta de uma soma ponderada de métricas que consideram o erro entre os sinais de saída do modelo otimizado e do de referência, a diferença quadrática entre seus parâmetros, e o custo em relação ao tempo e espaço necessários para executar o experimento. Portanto, a aplicação da metodologia proposta vem suprir a necessidade de estimar sistemas não lineares apropriadamente, encontrando um conjunto de parâmetros capaz de generalizar o comportamento do sistema real, através de um sinal de excitação que cumpra requisitos práticos do processo. A eficácia da metodologia proposta é analisada em detalhes através de resultados obtidos utilizando sistemas de fluídos, sistemas caóticos e de robótica móvel, tanto sobre rodas quanto subaquática. / The present work proposes a novel methodology for Sub-Optimal Excitation Signal Generation and Optimal Parameter Estimation of nonlinear systems. It is proposed that the evaluation of each signal must to take into account, among other factors, the difference between real system parameters and the obtained by estimation. However, this metric is not trivially obtained once the real parameters values are unknown. To do so it is adopted the hypothesis that, if the system can be fairly approximate by a white box model, it is possible to use this model as a benchmark to indicate the impact of a signal on a parametric estimation. In this way, the method uses an optimization methodology divided into two levels: (i) Inner Level; For a given excitation signal a nonlinear optimization method searches for the optimal set of parameters that minimizes the error between the output signals of the original and the benchmark models. (ii) At the outer level, an optimization method based on metaheuristics is responsible for finding the best excitation signal, based on the cost function composed of a weighted sum of metrics, that considers the error between the output signals of the optimized model and the benchmark, the quadratic difference between its parameters, and the cost in relation to the time and space required to execute the experiment. Thus, the application of the proposed methodology comes to supply the need to estimate nonlinear systems appropriately, finding a set of parameters capable of generalizing the behavior of the real system, through an excitation signal that fulfills practical requirements of the process. The proposed methodology is analyzed in detail through results obtained using fluid systems, chaotic systems and mobile robotics, both wheeled and underwater.

Dado um espaço localmente compacto Hausdorff K e um espaço de Banach X, Co(K,X) representa o espaço de Banach das funções contínuas em K com valores em X que se anulam no infinito com a norma do supremo. No presente trabalho, unificaremos e melhoraremos várias generalizações do teorema clássico de Banach-Stone para os espaços Co(K,X) devidas a Cambern, Amir, Behrends e Jarosz. No caso em que X=lp com $ 2 p, nossos resultados são maximais. / Let K be a locally compact Hausdor space and X a Banach space. By Co(K,X) we denote the Banach space of all X-valued continuous functions dened on K which vanish at innity, provided with the supremum norm. In the present work, we unify and strengthen several generalizations obtained in recent years of the classical Banach-Stone theorem for Co(K,X) spaces. In the case where X = lp such that 2 p < 1, our results are optimal.

Ce mémoire de thèse présente une méthode permettant d'améliorer laconduite automobile. Le filtre de Kalman étendu est utilisé pour identifierun modèle de la voiture. Ce filtre est particulièrement étudié afin de prendreen compte la redondance des informations et leur mesure asynchrone.Un ensemble cohérent et bon marché de capteurs - incluant accéléromètres,GPS, temps d'ouverture des injecteurs et vitesse - a été développé et installédans plusieurs véhicules. Ces mesures sont utilisées afin de reconstituer lafonction d'efficacité du moteur. Cette méthodologie peut-être utilisée pourtoute étude requérant la connaissance de cette fonction.La fonction d'efficacité est approchée par une fonction polynomiale etle modèle obtenu est la base d'une optimisation utilisant le principe dumaximum de Pontryagin.Les résultats des tests en condition réelle sont donnés et montrent l'efficicacité de l'observateur et du contrôleur / The PhD presents a combined approach to improving individual car efficiency. An optimal observer, the Extended Kalman Filter, is used to create an efficiency model for the car. Particular attention was paid to handling the asynchronous and redundant nature of the measurement data. A low-cost sensor suite developed to measure data is described. This sensor suite was installed on multiple vehicles to good success. It employsan accelerometer, gps, fuel injector timer, and Vss input to measure all the data necessary to reconstruct the car's state. This observer and sensor suite can be used as the base for any study which requires car efficiency maps, allowing research to proceed without manufacturer supplied data. Once the efficiency map is found, it is then curve-fitted in order to reduce model complexity. The simplified model is then used as a basis for optimal control through Pontryagin's Maximum Principle. Real-world test results are given, both for efficiency mapping, and for optimal control. Detailed discussion of the observer and controller is presented, in order to ease understanding and save implementation time

Magister Commercii - MCom / As a result of high economic inequality, widespread discontent with excessive chief executive officer (CEO) compensation levels is acute in South Africa (SA). Some commentators argue that instead of high levels of CEO pay causing inequality, it may be part of the solution if higher levels of CEO compensation translate into better company performance, so reducing unemployment. International studies investigating the relationship between CEO short-term cash compensation and current company performance generally report a weak or no relationship where accounting based measures of performance are used. Developments in the international literature reflect a stronger relationship when long-term incentive compensation (LIC) is included and total shareholder return (TSR) used to measure company performance. However, a concerning negative association between the highest paid CEOs in terms of excess LIC and future abnormal TSR is reported. In contrast, SA pay-performance research is largely not reflective of the developments in the international literature, with local studies mostly finding no pay-performance relationship, except where size-related accounting measures are used. As a result of the strong correlation between CEO pay and company size reported in the international literature, and local studies not adequately controlling for company size, the accuracy of the conclusions drawn in prior studies on the pay-performance sensitivity relationship in SA are brought into question. This study addresses the gaps in the SA literature by investigating the relationship between the size-adjusted excess CEO compensation and future abnormal TSR for the top 100 SA companies listed on the Johannesburg Stock Exchange for the period 2011 to 2013. A positive relationship is found between future abnormal TSR and short-term cash compensation, but not LIC. The levels and structure of CEO compensation in SA is also described.

Background: When asked what a desirable fertility level for populations might be, most politicians, journalists, and even social scientists would say it is around two children per woman, a level that has been labelled by demographers "replacement-level fertility." The reasons given for considering this level of fertility as something to aim at usually include maintaining the size of the labour force and stabilizing the old-age-dependency ratio. Objective: In this paper, we scrutinize this wide-spread view by introducing education in addition to age and sex as a further relevant source of observable population heterogeneity. We consider several criteria for assessing the long-term implications of alternative fertility levels and present numerical simulations with a view on minimizing the education-weighted total dependency ratio and complement this with the goal of reducing the amount of greenhouse gas emission in the context of climate change. Methods: We perform thousands of alternative simulations for different fertility levels (assumed to be constant over time) starting from empirically given population structures and derive the rate of fertility which yields the lowest level of our education-weighted dependency ratio. We study the sensitivity of our results to different parameter values and choose to focus on the actual populations of Europe and China over the course of the 21st century. Results: The results show that when education is assumed to present a cost at young age and results in higher productivity during adult age, then the fertility rate that on the long run keeps dependency at a minimum turns out to lie well below replacement fertility both in Europe and in China under a set of plausible assumptions. The optimal fertility level falls even lower when climate change is factored in as well. Conclusions: We conclude that there is nothing magical or particularly desirable about replacement level fertility. (authors' abstract)

Après une introduction générale et un survey de littérature, l’apport de cette thèse est d’établir un lien entre le marché des biens et le marché de travail et de proposer un système légal optimal pour dissuader les comportements opportunistes au sein de l’entreprise. Tout au long de la thèse, le cadre d’analyse utilisé est le cas d’un monopole qui produit deux types de biens. Les consommateurs sont hétérogènes selon leurs préférences à la qualité. Le chapitre 2 analyse différentes structures d’agence afin de déterminer la meilleure structure qui permet à la fois de maximiser le profit de l’entreprise et de maximiser le bien-être des consommateurs et des employés. Le chapitre 3 examine la distorsion de la qualité des biens et du niveau d’effort des employés en asymétrie d’information avec sélection adverse sur le marché des biens et le marché de travail par rapport à l’information parfaite. Le chapitre 4 étend le chapitre 3 en étudiant la même problématique avec un problème d’aléa-moral sur le marché de travail en présence d’une collusion entre le superviseur et l’employé. Ce chapitre questionne le rôle du consommateur et du juge à dissuader cette forme de comportement opportuniste. / After a general introduction and a survey of literature, the contribution of this thesis is to establish a link between the goods market and the labor market and to propose optimal legal system to deter opportunistic behavior within the company. Throughout the thesis, we consider a monopoly that produces two types of good. Consumers are heterogeneous according to their preferences to quality. Chapter 2 analyzes different agency structures to determine the best structure that allows both to maximize the profit of the company and maximize the welfare of consumers and employees. Chapter 3 examines distortion of the quality of goods and the level of the workers’ effort with adverse selection on the goods market and the labor market compared with perfect information. This chapter examines the role of the consumer and the judge to discourage this kind of opportunistic behavior.Keywords: Quality of goods, quality of labor, optimal contract, portfolio of contract, opportunism, collusion, social welfare, optimal sanctions, firm design, law and economics.

Variable Horizon Model Predictive Control (VH-MPC) is a form of predictive control that includes the horizon length as a decision variable in the constrained optimisation problem solved at each iteration. It has been recently applied to completion problems, where the system state is to be steered to a closed set in finite time. The behaviour of the system once completion has occurred is not considered part of the control problem. This thesis is concerned with three aspects of robustness and optimality in VH-MPC completion problems. In particular, the thesis investigates robustness to well defined but unpredictable changes in system and controller parameters, robustness to bounded disturbances in the presence of certain input parameterisations to reduce computational complexity, and optimal robustness to bounded disturbances using tightened constraints. In the context of linear time invariant systems, new theoretical contributions and algorithms are developed. Firstly, changing dynamics, constraints and control objectives are addressed by introducing the notion of feasible contingencies. A novel algorithm is proposed that introduces extra prediction variables to ensure that anticipated new control objectives are always feasible, under changed system parameters. In addition, a modified constraint tightening formulation is introduced to provide robust completion in the presence of bounded disturbances. Different contingency scenarios are presented and numerical simulations demonstrate the formulation’s efficacy. Next, complexity reduction is considered, using a form of input parameterisation known as move blocking. After introducing a new notation for move blocking, algorithms are presented for designing a move-blocked VH-MPC controller. Constraints are tightened in a novel way for robustness, whilst ensuring that guarantees of recursive feasibility and finite-time completion are preserved. Simulations are used to illustrate the effect of an example blocking scheme on computation time, closed-loop cost, control inputs and state trajectories. Attention is now turned towards mitigating the effect of constraint tightening policies on a VH-MPC controller’s region of attraction. An optimisation problem is formulated to maximise the volume of an inner approximation to the region of attraction, parameterised in terms of the tightening policy. Alternative heuristic approaches are also proposed to deal with high state dimensions. Numerical examples show that the new technique produces substantially improved regions of attraction in comparison to other proposed approaches, and greatly reduces the maximum required prediction horizon length for a given application. Finally, a case study is presented to illustrate the application of the new theory developed in this thesis to a non-trivial example system. A simplified nonlinear surface excavation machine and material model is developed for this purpose. The model is stabilised with an inner-loop controller, following which a VH-MPC controller for autonomous trajectory generation is designed using a discretised, linearised model of the stabilised system. Realistic simulated trajectories are obtained from applying the controller to the stabilised system and incorporating the ideas developed in this thesis. These ideas improve the applicability and computational tractability of VH-MPC, for both traditional applications as well as those that go beyond the realm of vehicle manœuvring.