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The fractal operators discussed in this dissertation are introduced in the form originally proposed in an earlier book of the candidate, which proves to be very convenient for physicists, due to its heuristic and intuitive nature. This dissertation proves that these fractal operators are the most convenient tools to address a number of problems in condensed matter, in accordance with the point of view of many other authors, and with the earlier book of the candidate. The microscopic foundation of the fractal calculus on the basis of either classical or quantum mechanics is still unknown, and the second part of this dissertation aims at this important task. This dissertation proves that the adoption of a master equation approach, and so of probabilistic as well as dynamical argument yields a satisfactory solution of the problem, as shown in a work by the candidate already published. At the same time, this dissertation shows that the foundation of Levy statistics is compatible with ordinary statistical mechanics and thermodynamics. The problem of the connection with the Kolmogorov-Sinai entropy is a delicate problem that, however, can be successfully solved. The derivation from a microscopic Liouville-like approach based on densities, however, is shown to be impossible. This dissertation, in fact, establishes the existence of a striking conflict between densities and trajectories. The third part of this dissertation is devoted to establishing the consequences of the conflict between trajectories and densities in quantum mechanics, and triggers a search for the experimental assessment of spontaneous wave-function collapses. The research work of this dissertation has been the object of several papers and two books.

Counterparty credit risk (CCR) is the risk that a counterparty in a deal will not be able to meet their contractual obligations in the future. While CCR is an important task for any risk desk, it has often been underestimated due to the miss-conception that some counterparties were deemed to be either too big to fail or too big to be allowed to default. This was highlighted by the 2008 nancial crisis that saw respected banks, such as Lehman Brothers, and nancial service providers, such as AIG, default on their obligations. Since then there has been renewed interest in CCR, with the focus being on actively pricing and hedging it. In this work CCR is invistigated including its intersection with other forms of risk. CCR mitigation techniques are explored, followed by the formal quanti cation of CCR in the form of credit value adjustments (CVA). The analysis of CCR is then applied to interest rate derivatives, more speci cally forward rate agreements (FRAs) and interest rate swaps (IRSs). The e ect of correlation on unilateral and bilateral CVA between counterparties, including risk factors such as the interest rate, is investigated. This is invistigated under two credit risk modelling frameworks, the structural and intensity based frameworks. It is shown that correlation has a none-negligible e ect on both unilateral and bilateral CVA for FRAs and IRSs. Correlation structures, namely the Gaussian and the Student-t copula, are used to induce dependency in order to understand their e ect on both unilateral and bilateral CVA. It is shown that the choice of copula does not have signi cant e ect on either unilateral or bilateral CVA.

Orientador: Edvaldo Assunção / Banca: Marcelo Carvalho M. Teixeira / Banca: Hilton Cleber Pietrobom / Resumo: Este trabalho aborda técnicas de controle em sistemas lineares realimentados com a derivada dos estados. Apresenta-se uma nova técnica de alocação de pólos, de forma que a resposta do sistema em malha fechada atenda alguns índices de desempenho. O projeto para o controlador é desenvolvido na forma de LMIs. Esse tipo de projeto é mais flexível no tratamento de robustez. Porém, é bem complicado inserir restriçõesi clássicas de índice de desempenho em LMIs. Para resolver essa situação usa-se o conceito de estabilidade regional (ou D-estabilidade) de sistemas. São apresentadas condições necessárias e suficientes para a D-estabilidade de sistemas lineares, realimentados com a derivada dos estados. Também são encontradas condições de suficiência para a D-estabilidade em sistemas com incertezas politópicas nos parâmetros. Apresenta-se a analogia que existe entre LMIs para sistemas com incertezas politópicas e LMIs para sistemas variantes no tempo. A eficiência da metodologia apresentada é avaliada através da solução de exemplos numéricos. / Abstract: This work focuses control techniques in linear systems using only state-derivative feed- back. It presents new techniques for pole-placement, where the transient response of a linear system is specified by design constraints. The design of the controller is described in LMI framework. This framework is more exible on the design of robust systems. However, it is more difficulty to incorporate classical design constraints in LMIs. The problem is solved using D-stability concept. We proposed necessary and sufficient condi- tions for D-stability of linear system using state derivative feedback. Are also proposed sufficient conditions to uncertain linear system and time-varying systems with bounded parameters. The validity and applicability of this approach are illustrated by examples. / Mestre

As for the Monte Carlo Method, we first introduce a brief history of the method and pricing options by using the method. Secondly, the basic idea of using the method in computing option price is described. Thirdly, pricing vanilla options is introduced. Fourthly, we discuss some techniques of improving computing accuracy. They include antithetic variables, control variate methods and importance sampling. / Fifth, we study in detail pricing option problems by using the Monte Carlo method. Then we present a new method on pricing American option, by which, the required memory in computation can be significantly reduced. For most methods of pricing American options, bias exists. However, by using the memory reduction method, minimizing biases is possible. We also discuss the problem for valuation of multiasset options by using our method. In fact, this is an important application of the Monte Carlo method in practical financial problems. / Finally, comparisons of the performances of these numerical results are presented. / Some basic concepts on options are first introduced. Then general methods for pricing options are described. These methods include: analytical formula, finite difference methods and binomial and multinomial methods. These prepare us for the in-depth study on the Monte Carlo method in subsequent chapters. / The Monte Carlo approach has proved to be a valuable and flexible computational tool in modern finance. The Monte Carlo method is the main topic of the thesis. / by Chen Yong. / "August 2002." / Adviser: Raymond Chan. / Source: Dissertation Abstracts International, Volume: 63-10, Section: B, page: 4710. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2002. / Includes bibliographical references (p. 77-79). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. Ann Arbor, MI : ProQuest dissertations and theses, [200-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. Ann Arbor, MI : ProQuest Information and Learning Company, [200-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstracts in English and Chinese. / School code: 1307.

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Main objective of this paper is to outline the use of derivative instruments for elimination of entity's risks with option of using so called hedge accounting. It uses international financial reporting standards (IFRS) as base, because it is the main "force" in this area nowadays and these standards are more or less used in national accounting standards as well. Core of this paper is identification of most used derivatives (types,frame,use) with a hint how to book them with application of hedge accounting. According to IFRS, there is also a need to test the effectiveness of the hedging using different methods. However, methods which should be used to test effectiveness of hedging are not specified so in the text you can find primary, most preferred methods with practical examples.

In antenna array processing it is generally required to enhance the reception or detection of a signal from a particular direction while suppressing noise and interference signals from other directions. An optimisation problem often posed to achieve this result is to minimise the array processor mean output power (or variance) subject to a fixed response in the array look direction. The look direction requirement can be met by imposing a set of linear constraints on the processor weights to yield what is known as the Linearly Constrained Minimum Variance (LCMV) processor. It has been found, however, that LCMV processors are susceptible to errors in the assumed direction of arrival of the desired signal. To achieve robustness against directional mismatch, additional constraints known as derivative constraints can be introduced. These constraints force the first and second order spatial derivatives of the array power response in the look direction to zero. However, constraints corresponding to necessary and sufficient (NS) conditions for these spatial derivatives to be zero are in general quadratic, and the resulting weight vector solution space is non-convex. One approach to this complex problem has been to consider conditions which are only sufficient for the spatial derivatives to be zero. Whilst this results in linear constraints, it exhibits certain anomalous behaviour, for example, dependence on the choice of array phase centre.Recent work in the area of derivative constraints has resulted in a method for efficiently solving the non-convex output power minimisation problem with quadratic derivative constraints. The optimisation problem addressed assumes that the input signal statistics and hence the input signal autocorrelation matrix R are known. In practice, R must be estimated from the receiver data.The main contribution of this thesis is the derivation of a ++ / new adaptive algorithm which implements an adaptive array processor with look direction plus 1st and 2nd order NS derivative constraints. The new algorithm is derived from the well-known Recursive Least Squares (RLS) technique but allows linear and quadratic constraints to be incorporated within the recursive framework. The algorithm offers the high performance characteristics associated with RLS methods, namely, fast convergence and high steady-state accuracy. The work encompasses a study of the characteristics of the algorithm in terms of numerical robustness, convergence properties, tracking and computational complexity.The study of the numerical properties of the algorithm has led to the second important contribution of this thesis: the identification of a parameter which is central to the numerical stability of the algorithm in a practical fixed precision environment. We show that this parameter is bounded during stable operation and can therefore be used to detect the onset of numerical instability within the algorithm. In addition, we show how existing techniques can be used to significantly improve the numerical robustness of the algorithm.Another important contribution of the thesis stems from an investigation into the multimodal nature of the quadratic, equality constrained optimisation problem resulting from the use of second order NS derivative constraints. In particular, we show that for a linear antenna array operating under certain conditions, the complex multimodal optimisation problem can be greatly simplified. This has important implications in both optimum and adaptive array signal processing.

This thesis is concerned with the designing of an nth order adaptive integral variable structure derivative estimator (AIVSDE). The proposed estimator's scheme is in fact a modified and extended version of the existing AIVSDE. The new proposed AIVSDE can be used as a direct nth differentiator for a smooth signal which has n continuous and bounded derivatives. The adaptive algorithm is utilized for the switching gain to remove the requirement for a priori knowledge about the upper bound of the derivative of the input signal. The stability of the redesigned first order, the second order, and the nth order derivative's estimation is guaranteed by the proposed scheme. An example is demonstrated for showing the applicability of the proposed AIVSDE.

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