This dissertation includes three chapters. The first chapter studies the question of whether countries with different fiscal capacity should optimally have different ex-ante minimum bank capital requirements. In an environment with endogenously incomplete markets and overinvestment because of moral hazard and pecuniary externalities, I show that countries with larger fiscal capacity should have lower minimum ex-ante bank capital requirements. I also show that, in addition to the minimum capital requirement, regulators in countries with a concentrated financial sector and large fiscal capacity (which are also countries with strong moral hazard) should impose a limit on the amount of liquidity pledged by financial institutions in a crisis state (for example, restrict the amount of put options/CDS contracts sold by financial institutions). The second chapter studies the welfare implications of a concentrated, imperfectly competitive banking sector, which faces a bank net worth constraint in a small open economy (SOE) environment. There are two standard sources of inefficiency --- pecuniary externalities, which lead to overinvestment, and a standard monopolistic underinvestment force. I show that the optimal policy instruments include subsidies on firm borrowing costs in certain periods and capital account controls in others, which is a good proxy for the behavior of emerging markets. For every country, there exists a financial sector with a particular banking sector concentration, for which the inefficiencies offset each other and no government intervention is required in some periods. Furthermore, this paper documents a novel theoretical result --- the interaction between future binding bank net worth constraints and dynamic (future) underinvestment could lead to ex-ante overinvestment even in economies with a single monopolistic bank where there are no pecuniary externalities. The last third chapter, which is coauthored with Kenneth Rogoff, evaluates a new class of exchange rate forecasting studies, which claim that structural models are getting closer to being able to forecast exchange rates at short horizons. We argue that misinterpretation of some new out-of-sample tests for nested models, over-reliance on asymptotic test statistics, and failure to sufficiently check robustness to alternative time windows have led many studies to overstate even the relatively thin positive results that have been found. / Economics

Time-optimal solutions provide us with the fastest means to regulate a system in presence of input constraints. This advantage of time-optimal control solutions is offset by the fact that their real-time implementation involves computationally intensive iterative techniques. Moreover, time-optimal controls depend on the initial state and have to be recalculated for even the slightest perturbation. Clearly time-optimal controls are not good candidates for online regulation. Consequently, the search for alternatives to time-optimal solutions is a very active area of research. The work described here is inspired by the simplicity of optimal-aim concept. The "optimal-aim strategies" provide online regulation in presence of bounded inputs with minimal computational effort. These are based purely on state-space geometry of the plant and are inherently adaptive in nature. Optimal-aim techniques involve aiming of trajectory derivative (or the state velocity vector) so as to approach the equilibrium state in the best possible manner. This thesis documents the efforts to develop an online regulation algorithm for systems with input constraints. Through a number of hypotheses focussed on trying to reproduce the exact time-optimal solution, the diffculty associated with this task is demonstrated. A modification of optimal-aim concept is employed to develop a novel regulation algorithm. In this algorithm, aim directions are chosen in a special manner to generate the time-optimal control approximately. The control scheme thus developed is shown to be globally stabilizing for systems having eigenvalues in the CLHP (closed left half-plane). It is expected that this method or its modifications can be extended to higher dimensional systems as a part of future research. An alternative control algorithm involving a simple state-space aiming concept is also developed and discussed.

Many insurance and finance activities involve multiple risks. Dependence structures between different risks play an important role in both theoretical models and practical applications. However, stochastic and actuarial models with dependence are very challenging research topics. In most literature, only special dependence structures have been considered. However, most existing special dependence structures can be integrated into more-general contexts. This thesis is motivated by the desire to develop more-general dependence structures and to consider their applications. This thesis systematically studies different dependence notions and explores their applications in the fields of insurance and finance. It contributes to the current literature in the following three main respects. First, it introduces some dependence notions to actuarial science and initiates a new approach to studying optimal reinsurance problems. Second, it proposes new notions of dependence and provides a general context for the studies of optimal allocation problems in insurance and finance. Third, it builds the connections between copulas and the proposed dependence notions, thus enabling the constructions of the proposed dependence structures and enhancing their applicability in practice. The results derived in the thesis not only unify and generalize the existing studies of optimization problems in insurance and finance, but also admit promising applications in other fields, such as operations research and risk management.

Power outages usually lead to customer complaints and revenue losses. Consequently, fast and accurate fault location on electric lines is needed so that repair work can be carried out as fast as possible. Chapter 2 describes novel fault location algorithms for radial and non-radial ungrounded power distribution systems. For both types of systems, fault location approaches using line to neutral or line to line measurements are presented. It’s assumed that network structure and parameters are known, so that during-fault bus impedance matrix of the system can be derived. Functions of bus impedance matrix and available measurements at substation are formulated, from which the unknown fault location can be estimated. Evaluation studies on fault location accuracy and robustness of fault location methods to load variations and measurement errors has been performed. Most existing fault location methods rely on measurements obtained from meters installed in power systems. To get the most from a limited number of meters available, optimal meter placement methods are needed. Chapter 3 presents a novel optimal meter placement algorithm to keep the system observable in terms of fault location determination. The observability of a fault location in power systems is defined first. Then, fault location observability analysis of the whole system is performed to determine the least number of meters needed and their best locations to achieve fault location observability. Case studies on fault location observability with limited meters are presented. Optimal meter deployment results based on the studied system with equal and varying monitoring cost for meters are displayed. To enhance fault location accuracy, an optimal fault location estimator for power distribution systems with distributed generation (DG) is described in Chapter 4. Voltages and currents at locations with power generation are adopted to give the best estimation of variables including measurements, fault location and fault resistances. Chi-square test is employed to detect and identify bad measurement. Evaluation studies are carried out to validate the effectiveness of optimal fault location estimator. A set of measurements with one bad measurement is utilized to test if a bad data can be identified successfully by the presented method.

The purpose of this thesis is to look into the difficulty of valuing American options, put as well as call, on an asset that pays continuous dividends. The authors are willing to demonstrate how mentioned above securities can be priced using a simple approximation of the Kim integral equations by quadrature formulas. This approach is compared with closed form American Option price formula proposed by Bjerksund-Stenslands in 2002. The results obtained by Bjerksund-Stenslands method are numerically compared by authors to the Kim’s. In Joon Kim’s approximation seems to be more accurate and closer to the chosen “true” value of an American option, however, Bjerksund-Stenslands model is demonstrating a higher speed in calculations.

Συστήματα μαγνητικών ταινιών χρησιμοποιούνται ευρέως ως μέσα αποθήκευσης και αποκατάστασης δεδομένων. Λόγω του χαμηλού τους κόστους αναλογικά των σκληρών δίσκων συνεχίζουν να προτιμούνται σε μεγάλο πλήθος εφαρμογών όπως δευτερεύουσες συσκευές αποθήκευσης, εγγραφής και επεξεργασίας ηχητικών δεδομένων,βιντεοκάμερες κ.ά. Σε περιπτώσεις όπου θέλουμε να επεξεργαστούμε μια μαγνητοταινία για γρήγορη μεταφορά ή εγγραφή δεδομένων θα πρέπει -η ταινία- να μεταφέρεται σε υψηλή ταχύτητα από το μηχανισμό του συστήματος. Η ταχύτητα αυτή να διατηρείται σταθερή και να βρίσκεται σε συγχρονισμό ε την κεφαλή ανάγνωσης/εγγραφής προς αποφυγή σφαλμάτων μεταφοράς και αναγνώρισης δεδομένων, αναπηδήσεων και χρονικών σφαλμάτων. Σε πιθανά σφάλματα η επαναφορά της ταινίας στο επιθυμητό σημείο αποτελεί τη λύση για την αποκατάσταση του σφάλματος. Η επιτάχυνση και επιβράδυνση που δέχεται η ταινία σε κάθε γρήγορη αναζήτηση δεδομένων προκαλούν τη μεγαλύτερη επιβάρυνση σε αυτή. Ειδικά η συχνή επανατοποθέτηση της ταινίας στο ίδιο ση είο λόγω της βαθμιαίας εξασθένισης του σήματος ανάγνωσης. Σκοπός είναι ο σχεδιασμός ενός μηχανισμού εταφοράς της ταινίας ο οποίος προσφέρει μια ικανοποιητική τάση στην ταινία όπως και ταχύτητα μεταφοράς αυτής. / Optimal control and estimation of a magnetic tape-drive system.

Le transport optimal trouve un nombre grandissant d’applications, dont celle qui nous intéresse dans ce travail, l'interpolation d’images. Malgré cet essor, la résolution numérique de ce transport soulève des difficultés et le développement d’algorithmes efficaces reste un problème d'actualité, en particulier pour des images de grande taille, comme on en trouve dans certains domaines (météorologie,...).Nous nous intéressons dans ce travail à la formulation de Benamou et Brenier, qui ont placé le problème dans un contexte de mécanique des milieux continus en ajoutant une dimension temporelle. Leur formulation consiste en la minimisation d’une fonctionnelle sur un espace des contraintes contenant une condition de divergence nulle, et les algorithmes existants utilisent une projection sur cet espace.A l'opposé, dans cette thèse, nous définissons et mettons en oeuvre des algorithmes travaillant directement dans cet espace.En effet, nous montrons que la fonctionnelle a de meilleures propriétés de convexité sur celui-ci.Pour travailler dans cet espace, nous considérons trois représentations des champs de vecteurs à divergence nulle. La première est une base d’ondelettes à divergence nulle. Cette formulation a été implémentée numériquement dans le cas des ondelettes périodiques à l'aide d'une descente de gradient, menant à un algorithme de convergence lente mais validant la faisabilité de la méthode. La deuxième approche consiste à représenter les vecteurs à divergence nulle par leur fonction de courant munie d'un relèvement des conditions au bord et la troisième à utiliser la décomposition de Helmholtz-Hodge.Nous montrons de plus que dans le cas unidimensionnel en espace, en utilisant l’une ou l'autre de ces deux dernières représentations, nous nous ramenons à la résolution d’une équation de type courbure minimale sur chaque ligne de niveau du potentiel, munie des conditions de Dirichlet appropriées.La minimisation de la fonctionnelle est alors assurée par un algorithme primal-dual pour problèmes convexes de Chambolle-Pock, qui peut aisément être adapté à nos différentes formulations et est facilement parallèlisable, menant à une implémentation performante et simple.En outre, nous démontrons les gains significatifs de nos algorithmes par rapport à l’état de l’art et leur application sur des images de taille réelle. / Optimal transport has an increasing number of applications, including image interpolation, which we study in this work. Yet, numerical resolution is still challenging, especially for real size images found in applications.We are interested in the Benamou and Brenier formulation, which rephrases the problem in the context of fluid mechanics by adding a time dimension.It is based on the minimization of a functional on a constraint space, containing a divergence free constraint and the existing algorithms require a projection onto the divergence-free constraint at each iteration.In this thesis, we propose to work directly in the space of constraints for the functional to minimize.Indeed, we prove that the functional we consider has better convexity properties on the set of constraints.To work in this space, we use three different divergence-free vector decompositions. The first in which we got interested is a divergence-free wavelet base. This formulation has been implemented numerically using periodic wavelets and a gradient descent, which lead to an algorithm with a slow convergence but validating the practicability of the method.First, we represented the divergence-free vector fields by their stream function, then we studied the Helmholtz-Hodge decompositions. We prove that both these representations lead to a new formulation of the problem, which in 1D + time, is equivalent to the resolution of a minimal surface equation on every level set of the potential, equipped with appropriate Dirichlet boundary conditions.We use a primal dual algorithm for convex problems developed by Chambolle and Pock, which can be easily adapted to our formulations and can be easily sped up on parallel architectures. Therefore our method will also provide a fast algorithm, simple to implement.Moreover, we show numerical experiments which demonstrate that our algorithms are faster than state of the art methods and efficient with real-sized images.

La manipulation aérienne a été un domaine de recherche actif ces dernières années, principalement parce que les applications actives des véhicules aériens autonomes (UAV en anglais), augmente l'employabilité de ces véhicules pour diverses applications.Le développement récent de la manipulation aérienne a trouvé des applications potentielles dans les deux domaines, militaires et civils. Les applications militaires incluent le patrouilleur des frontières, la détection des mines, la reconnaissance, etc., tandis que les applications civiles sont en matière de gestion des catastrophes, d'inspection des ponts, de construction, de livraison de matériel, de recherche et de sauvetage, etc.La recherche sur la robotique aérienne implique principalement des hélicoptères et des architectures de décollage et d'atterrissage verticales (VTOL). Le principal avantage de ces plates-formes est leur maniabilité et la capacité d'effectuer des vols stationnaires, ce qui est essentiel pour les applications. Cette thèse porte sur les avions VTOL, où l'hélicoptère à quatre rotors ou quadrirotor est principalement étudié.En ce qui concerne le problème de la manipulation aérienne, la quantité d'applications augmente, mais en même temps, la complexité de la modélisation et du contrôle d'un tel système est également plus grande. L'un des plus grands défis réside dans leur charge utile limitée. Certaines approches ont essayé de résoudre le problème en utilisant plusieurs robots pour transporter des charges utiles avec des pinces ou des câbles, où leurs effecteurs et pinces doivent être légers eux-mêmes et capables de saisir des formes complexes. Un autre défi est que la dynamique du robot est considérablement modifiée par l'ajout de charges utiles. Cependant, pour le transport de la charge utile, il est nécessaire que les robots puissent estimer l'inertie de la charge utile et s'y adapter pour améliorer les performances de suivi.Selon les antécédents et les défis sur les véhicules VTOL portant des charges utiles ou des manipulateurs, la contribution du présent travail est centrée sur la modélisation et la conception d'une loi de commande non linéaire et une analyse de stabilité formelle pour la stabilisation asymptotique d'un véhicule VTOL portant un bras manipulateur. Pour cela, un modèle général d'un quadrirotor portant un bras manipulateur est proposé. Après cela, une loi de commande presque globalement asymptotique lisse pour la stabilisation de l'attitude qui prend en compte les effets de mouvement du bras est conçue. Une fois que le problème d'attitude est résolu, il est possible de concevoir un contrôleur non linéaire globalement asymptotique pour la dynamique de position basée sur l'utilisation de somme des fonctions saturés afin de prendre en compte les limitations des actionneurs. Enfin, certaines expériences pour valider les lois de commande proposées sont effectuées. / Aerial manipulation has been an active area of research in recent years, mainly because the active tasking of Unmanned Aerial Vehicles (UAV) increases the employability of these vehicles for various applications.The recent development of the aerial manipulation has found potential applications in both, military and civilian domains. Military applications include border patrolling, mine detection, reconnaissance, etc., while civilian applications are in disaster management, bridge inspection, construction, material delivery, search and rescue, etc.The research on aerial robotics has mainly involved helicopters and Vertical Take-off and Landing (VTOL) architectures. The main advantage of these platforms is theirmaneuverability and the capacity to perform hovers, which is essential for the applications. This thesis deals with VTOL aircrafts, where the four rotor helicopter, quadcopter or quadrotor is mainly studied.Regarding the problem of aerial manipulation, the amount of applications are increased, but at the same time the complexity of modeling and control of such a system are equally bigger. One of the biggest challenges arise from their limited payload. Some approaches have tried to solve the problem using multiple robots to carry payloads with grippers or with cables, where their end effectors and grippers have to be lightweight themselves and capable of grasping complex shapes. Another challenge is that the dynamics of the robot are significantly altered by the addition of payloads. However, for payload transport, it is necessary that the robots are able to estimate the inertia of the payload and adapt to it to improve tracking performance.According to the background and challenges on VTOL vehicles carrying payloads or manipulators, the contribution of the present work is centered on the modelling and the design of a nonlinear control and a formal stability analysis for the asymptotical stabilization of a VTOL vehicle carrying a manipulator arm. For this a general model of a quadcopter carrying a manipulator arm is proposed. After that, a smooth almost globally asymptotically control law for attitude stabilization which takes into account the arm motion effects is designed. Once the attitude problem is solved, it is possible to design a a globally asymptotically nonlinear controller for the translational dynamics based in the usage of nested and sum of saturation functions in order to take into account the actuators limitations. Finally, some experiments in order to validate the proposed control laws are carried out.

De type parabolique et soumis à l’action d’un couple de contrôles (h, k) où h et k jouent des rôles différents ; le contrôle k étant de type "contrôlabilité" et h de type "contrôle optimal".Il est alors naturel de considérer un problème d’optimisation multi-critères. Il existe plusieurs façons d’étudier de tels problèmes. Nous proposons, dans cette thèse, le contrôle de Stackelberg. Il s’agit d’une notion d’optimisation hiérarchique avec, ici, h qui est le "Leader" et k le "Follower". / In this thesis, we are interested in evolution problems governed by parabolic equations subjected to the action of a pair of controls (h, k) where h and k play different roles : the control k being of "controllability" type and h of "optimal control" type.It is then natural to consider a multi-criteria optimization problem. There are several ways to study such problems. We propose in this thesis, the Stackelberg control which is a notion of hierarchical optimization with here, h which is the "Leader" and k the "Follower".

Au début des années 2000, J. D. Benamou et Y. Brenier ont proposé une formulation dynamique du transport optimal basée sur la recherche en espace-temps d'une densité et d'une quantité de mouvement minimisant une énergie de déplacement entre deux densités. Ils ont alors proposé, pour la résolution numérique de ce problème, d'écrire ce dernier sous la forme d'une recherche de point selle d'un certain lagrangien via un algorithme de lagrangien augmenté. Nous étudierons, à l'aide de la théorie des opérateurs non-expansifs, la convergence de cet algorithme vers un point selle du lagrangien introduit, et ceci dans les conditions les plus générales possibles, en particulier dans les cas où les densités de départ et d'arrivée s'annulent sur certaines zones du domaine de transport. La principale difficulté de notre étude consistera en la preuve de l'existence d'un point selle, et surtout de l'unicité de la composante densité-quantité de mouvement dans de telles conditions. En effet, celles-ci impliquent de devoir traiter avec des plans de transport optimaux non réguliers : c'est pourquoi une importante partie de nos travaux aura pour objet une étude approfondie de la régularité d'un champ de vitesse associé à de tels plans de transport. Nous tenterons également de caractériser les propriétés d'un champ de vitesse associé à un plan de transport optimal dans l'espace quadratique. Pour finir, nous explorerons différentes approches relatives à l'introduction de contraintes physiques dans la formulation dynamique du transport optimal, basées sur une pénalisation du domaine de transport ou du champ de vitesse. / In the beginning of the 2000 years, J. D. Benamou and Y. Brenier have proposed a dynamical formulation of the optimal transport problem, corresponding to the time-space search of a density and a momentum minimizing a transport energy between two densities. They proposed, in order to solve this problem in practice, to deal with it by looking for a saddle point of some Lagrangian by an augmented Lagrangian algorithm. Using the theory of non-expansive operators, we will study the convergence of this algorithm to a saddle point of the Lagrangian introduced, in the most general feasible conditions, particularly in cases where initial and final densities are canceling on some areas of the transportation domain. The principal difficulty of our study will consist of the proof, in these conditions, of the existence of a saddle point, and especially in the uniqueness of the density-momentum component. Indeed, these conditions imply to have to deal with non-regular optimal transportation maps: that is why an important part of our works will have for object a detailed study of the properties of the velocity field associated to an optimal transportation map in quadratic space. To finish, we will explore different approaches for introducing physical priors in the dynamical formulation of optimal transport, based on penalization of the transportation domain or of the velocity field.