The objective of this thesis is to formulate a generic dictionary learning method with the guiding principle that states: Efficient representations lead to efficient estimations. The fundamental idea behind using transforms or dictionaries for signal representation is to exploit the regularity within data samples such that the redundancy of the representation is minimized subject to a level of fidelity. This observation translates to rate-distortion cost in compression literature, where a transform that has the lowest rate-distortion cost provides a more efficient representation than the others. In our work, rather than using as an analysis tool, the rate-distortion cost is utilized to improve the efficiency of transforms. For this, an iterative optimization method is proposed, which seeks an orthonormal transform that reduces the expected value of rate-distortion cost of an ensemble of data. Due to the generic nature of the new optimization method, one can design a set of orthonormal transforms either in the original signal domain or on the top of a transform-domain representation. To test this claim, several image codecs are designed, which use block-, lapped- and wavelet-transform structures. Significant increases in compression performances are observed compared to original methods. An extension of the proposed optimization method for video coding gave us state-of-the-art compression results with separable transforms. Also using the robust statistics, an explanation to the superiority of new design over other learning-based methods such as Karhunen-Loeve transform is provided. Finally, the new optimization method and the minimization of the "oracle" risk of diagonal estimators in signal estimation is shown to be equal. With the design of new diagonal estimators and the risk-minimization-based adaptation, a new image denoising algorithm is proposed. While these diagonal estimators denoise local image patches, by formulation the optimal fusion of overlapping local denoised estimates, the new denoising algorithm is scaled to operate on large images. In our experiments, the state-of-the-art results for transform-domain denoising are achieved.

In this thesis we provide a unifying framework for two decades of work in an area of Machine Learning known as cost-sensitive Boosting algorithms. This area is concerned with the fact that most real-world prediction problems are asymmetric, in the sense that different types of errors incur different costs. Adaptive Boosting (AdaBoost) is one of the most well-studied and utilised algorithms in the field of Machine Learning, with a rich theoretical depth as well as practical uptake across numerous industries. However, its inability to handle asymmetric tasks has been the subject of much criticism. As a result, numerous cost-sensitive modifications of the original algorithm have been proposed. Each of these has its own motivations, and its own claims to superiority. With a thorough analysis of the literature 1997-2016, we find 15 distinct cost-sensitive Boosting variants - discounting minor variations. We critique the literature using {\em four} powerful theoretical frameworks: Bayesian decision theory, the functional gradient descent view, margin theory, and probabilistic modelling. From each framework, we derive a set of properties which must be obeyed by boosting algorithms. We find that only 3 of the published Adaboost variants are consistent with the rules of all the frameworks - and even they require their outputs to be calibrated to achieve this. Experiments on 18 datasets, across 21 degrees of cost asymmetry, all support the hypothesis - showing that once calibrated, the three variants perform equivalently, outperforming all others. Our final recommendation - based on theoretical soundness, simplicity, flexibility and performance - is to use the original Adaboost algorithm albeit with a shifted decision threshold and calibrated probability estimates. The conclusion is that novel cost-sensitive boosting algorithms are unnecessary if proper calibration is applied to the original.

Исследование предлагает совершенствование методов регулирования кредитного риска. Банковским учреждениям предложено повысить качество экспертной оценки потенциального клиента-заёмщика посредством внесения дополнений в систему мотивации сотрудников и включение коэффициента внутренней рентабельности в оценку мотивации персонала. Предложена модифицированная модель оценки вероятности банкротства и применение коэффициентов оценки кредитоспособности исходя из отраслевой принадлежности предприятия. / The study suggests improving the methods of credit risk regulation. It was proposed to banking institutions to improve the quality of the expert assessment of a potential client-borrower by introducing additions to the employee motivation system and including the internal profitability ratio in the assessment of staff motivation. A modified model for assessing the probability of bankruptcy and the use of coefficients for assessing creditworthiness based on the sectoral affiliation of the enterprise are proposed.

Cette thèse porte sur les questions d'évaluation et de couverture des options dans un modèle exponentiel-Lévy avec changements de régime. Un tel modèle est construit sur un processus additif markovien un peu comme le modèle de Black- Scholes est basé sur un mouvement Brownien. Du fait de l'existence de plusieurs sources d'aléa, nous sommes en présence d'un marché incomplet et ce fait rend inopérant les développements théoriques initiés par Black et Scholes et Merton dans le cadre d'un marché complet. Nous montrons dans cette thèse que l'utilisation de certains résultats de la théorie des processus additifs markoviens permet d'apporter des solutions aux problèmes d'évaluation et de couverture des options. Notamment, nous arrivons à caracté- riser la mesure martingale qui minimise l'entropie relative à la mesure de probabilit é historique ; aussi nous dérivons explicitement sous certaines conditions, le portefeuille optimal qui permet à un agent de minimiser localement le risque quadratique associé. Par ailleurs, dans une perspective plus pratique nous caract érisons le prix d'une option Européenne comme l'unique solution de viscosité d'un système d'équations intégro-di érentielles non-linéaires. Il s'agit là d'un premier pas pour la construction des schémas numériques pour approcher ledit prix. / This thesis focuses on the pricing and hedging problems of financial derivatives in a Markov-modulated exponential-Lévy model. Such model is built on a Markov additive process as much as the Black-Scholes model is based on Brownian motion. Since there exist many sources of randomness, we are dealing with an incomplete market and this makes inoperative techniques initiated by Black, Scholes and Merton in the context of a complete market. We show that, by using some results of the theory of Markov additive processes it is possible to provide solutions to the previous problems. In particular, we characterize the martingale measure which minimizes the relative entropy with respect to the physical probability measure. Also under some conditions, we derive explicitly the optimal portfolio which allows an agent to minimize the local quadratic risk associated. Furthermore, in a more practical perspective we characterize the price of a European type option as the unique viscosity solution of a system of nonlinear integro-di erential equations. This is a rst step towards the construction of e ective numerical schemes to approximate options price.

Made available in DSpace on 2016-04-25T18:40:30Z (GMT). No. of bitstreams: 1 Amaury de Souza Amaral.pdf: 4071869 bytes, checksum: d9dc83b1b016fbb7b489442f44ce1071 (MD5) Previous issue date: 2008-05-26 / In this work, one presents different enterprise valuation models and approaches, like the discounted free cash flow, the EVA model and all the way up to more recent option pricing theory of applied equity capital valuation. This last theory (options pricing theory) is believed to be the best theory that better qualifies the value of an enterprise. It is based on the premises that the enterprise value can be based on the debt market value and the equity capital where the accumulated amounts can be negotiated. This project presents models developed by Arzac (2005) about enterprise valuation in continuous -time formulation, regarding the revenue as an underlying asset of the option theory, where a hedged portfolio is built (with the same logic as the Black-Scholes model). The revenue presents stochastic behavior, represented by a brownian motion, providing reasonable representation of the revenues behavior. Furthermore, the best moment to enter in a firm is evaluated, establishing the revenue value that makes safe realize an investment. After that, the enterprise value is determined in that case that the possibility to enter and exit the firm is considered when the revenue is not satisfactory. The possibility of re-entering the firm is also possible. At last, is presented the enterprise valuation with expansion possibility through new investments. Thus, a new approach to valuation of companies in uncertainty conditions is proposed, based on risk minimization theory of Bouchaud & Potters (2003), in that the revenue trajectory will directly influence the enterprise entry options. The study, that uses Arzac's mathematical approach (continuous-time formulation, building of riskless portfolio, etc.), proposes a less intuitive risk measurement based on recent past behavior, transforming the random process of the revenue (risk asset) in a process based on future tendencies of revenue in a probabilistic way and trajectory dependents / Este trabalho apresenta as diversas formas de avaliação de empresas em diferentes abordagens, dentre elas os modelos baseados em fluxos de caixa livre descontados, modelos baseados no EVA até chegar a teorias mais recentes como a teoria de precificação de opções aplicadas à avaliação de patrimônio líquido. Acredita-se ser esta última teoria a que mais se aproxima e melhor quantifica o valor de uma entidade. Parte-se da premissa de que o valor da empresa pode ser obtido pelo valor de mercado da dívida e do patrimônio líquido que acumuladamente podem ser negociados. O trabalho também apresenta modelos desenvolvidos por Arzac (2005), que versam sobre avaliação de empreendimentos com formulação em tempo contínuo, em que a receita é tratada como o ativo subjacente da teoria das opções que possibilita a construção de uma carteira replicante (com a mesma lógica do modelo de Black-Scholes). A receita apresenta um comportamento aleatório representado por um movimento browniano, que fornece uma representação razoável do comportamento da receita. Além disso, é avaliado o melhor momento de entrada em um negócio, estabelecendo-se qual o valor da receita a partir da qual é seguro a realização do investimento. Em seguida, é determinado o valor da entidade considerando-se a possibilidade de entrar em um neg´ocio e sair dele, caso o desempenho da receita não seja satisfatório, incluindo-se ainda a possibilidade de re-entrada. E finalmente a avaliação de empresas com possibilidade de expansão através de novos investimentos. Dessa forma, é proposta uma nova abordagem de avaliação de empreendimentos em condições de incerteza, inspirada nas teorias de minimização de risco propostas por Bouchaud e Potters (2003), em que as avalções das trajetórias das receitas irão influenciar diretamente as opções de entrada em um empreendimento. O estudo, que utiliza a abordagem matemática de Arzac (formulação em tempo contínuo, construção de carteiras replicantes, etc.), propõe uma medida de risco menos intuitiva baseada no comportamento do passado recente, transformando o processo aleatório do valor da receita da empresa (ativo de risco) em um processo que se baseie em tendências futuras de valores desta receita de forma probabilística e dependentes de uma trajetória

Cette thèse porte sur les questions d'évaluation et de couverture des options dans un modèle exponentiel-Lévy avec changements de régime. Un tel modèle est construit sur un processus additif markovien un peu comme le modèle de Black- Scholes est basé sur un mouvement Brownien. Du fait de l'existence de plusieurs sources d'aléa, nous sommes en présence d'un marché incomplet et ce fait rend inopérant les développements théoriques initiés par Black et Scholes et Merton dans le cadre d'un marché complet. Nous montrons dans cette thèse que l'utilisation de certains résultats de la théorie des processus additifs markoviens permet d'apporter des solutions aux problèmes d'évaluation et de couverture des options. Notamment, nous arrivons à caracté- riser la mesure martingale qui minimise l'entropie relative à la mesure de probabilit é historique ; aussi nous dérivons explicitement sous certaines conditions, le portefeuille optimal qui permet à un agent de minimiser localement le risque quadratique associé. Par ailleurs, dans une perspective plus pratique nous caract érisons le prix d'une option Européenne comme l'unique solution de viscosité d'un système d'équations intégro-di érentielles non-linéaires. Il s'agit là d'un premier pas pour la construction des schémas numériques pour approcher ledit prix. / This thesis focuses on the pricing and hedging problems of financial derivatives in a Markov-modulated exponential-Lévy model. Such model is built on a Markov additive process as much as the Black-Scholes model is based on Brownian motion. Since there exist many sources of randomness, we are dealing with an incomplete market and this makes inoperative techniques initiated by Black, Scholes and Merton in the context of a complete market. We show that, by using some results of the theory of Markov additive processes it is possible to provide solutions to the previous problems. In particular, we characterize the martingale measure which minimizes the relative entropy with respect to the physical probability measure. Also under some conditions, we derive explicitly the optimal portfolio which allows an agent to minimize the local quadratic risk associated. Furthermore, in a more practical perspective we characterize the price of a European type option as the unique viscosity solution of a system of nonlinear integro-di erential equations. This is a rst step towards the construction of e ective numerical schemes to approximate options price.

This dissertation mainly studies correlation and then portfolio analysis of financial contagion and capital flight, focusing on currency co-movements around the political uncertainty due to the Brexit referendum on 26 June 2016. The correlation, mean, and covariance computations in the analysis are both time-unconditional and time-conditional, and the generalized autoregressive conditional heteroskedasticity (GARCH) and exponentially weighted moving average (EWMA) methods are applied. The correlation analysis in this dissertation (Chapter 1) extends the previous literature on contagion testing based on a single global factor model, bivariate correlation analysis, and heteroskedasticity bias correction. Chapter 1 proposes an alternatively extended framework, assuming that intensification of financial correlations in a state of distress could coincide with rising global-factor-loading variability, provides simple tests to verify the assumptions of the literature and of the extended framework, and considers capital flight other than merely financial contagion. The outcomes show that, compared to the literature, the extended framework can be deemed more verified to the Brexit case. Empirically, with the UK being the shock-originating economy and the sterling value plummeting on the US dollar, there exist contagions to some other major currencies as well as a flight to quality, particularly to the yen, probably suggesting diversification benefits. When the correlation coefficients are time-conditional, or depend more on more recent data, the evidence shows fewer contagions and flights since the political uncertainty in question disappeared gradually over time. After relevant interest rates were partialled out, some previous statistical contagion and flight occurrences became less significant or even insignificant, possibly due to the significant impacts of the interest rates on the corresponding currency correlations. The portfolio analysis in this dissertation (Chapter 2) examines financial contagion and capital flight implied by portfolio reallocations through mean-variance portfolio analysis, and builds on the correlation analysis in Chapter 1. In the correlation analysis, correlations are bivariate, whereas in the portfolio analysis they are multivariate and the risk-return tradeoff is also vitally involved. Portfolio risk minimization and reward-to-risk maximization are the two analytical cases of portfolio optimality taken into consideration. Robust portfolio optimizations, using shrinkage estimations and newly proposed risk-based weight constraints, are also applied. The evidence demonstrates that the portfolio analysis outcomes regarding currency contagions and flights, implying diversification benefits, vary and are noticeably dissimilar from the correlation analysis outcomes of Chapter 1. Subsequently, it could be inferred that the diversification benefits deduced from the portfolio and correlation analyses differ owing to the dominance, during market uncertainty, of the behaviors of the means and (co)variances of all the shock-originating and shock-receiving returns, over the behaviors of just bivariate correlations between the shock-originating and shock-receiving returns. Moreover, corrections of the heteroskedasticity bias inherent in the shock-originating returns, overall, do not have an effect on currency portfolio rebalancing. Additionally, hedging demands could be implied from detected structural portfolio reallocations, probably as a result of variance-covariance shocks rising from Brexit. / This dissertation mainly studies correlation and then portfolio analysis of financial contagion and capital flight, focusing on currency co-movements around the political uncertainty due to the Brexit referendum on 26 June 2016. The correlation, mean, and covariance computations in the analysis are both time-unconditional and time-conditional, and the generalized autoregressive conditional heteroskedasticity (GARCH) and exponentially weighted moving average (EWMA) methods are applied. The correlation analysis in this dissertation (Chapter 1) extends the previous literature on contagion testing based on a single global factor model, bivariate correlation analysis, and heteroskedasticity bias correction. Chapter 1 proposes an alternatively extended framework, assuming that intensification of financial correlations in a state of distress could coincide with rising global-factor-loading variability, provides simple tests to verify the assumptions of the literature and of the extended framework, and considers capital flight other than merely financial contagion. The outcomes show that, compared to the literature, the extended framework can be deemed more verified to the Brexit case. Empirically, with the UK being the shock-originating economy and the sterling value plummeting on the US dollar, there exist contagions to some other major currencies as well as a flight to quality, particularly to the yen, probably suggesting diversification benefits. When the correlation coefficients are time-conditional, or depend more on more recent data, the evidence shows fewer contagions and flights since the political uncertainty in question disappeared gradually over time. After relevant interest rates were partialled out, some previous statistical contagion and flight occurrences became less significant or even insignificant, possibly due to the significant impacts of the interest rates on the corresponding currency correlations. The portfolio analysis in this dissertation (Chapter 2) examines financial contagion and capital flight implied by portfolio reallocations through mean-variance portfolio analysis, and builds on the correlation analysis in Chapter 1. In the correlation analysis, correlations are bivariate, whereas in the portfolio analysis they are multivariate and the risk-return tradeoff is also vitally involved. Portfolio risk minimization and reward-to-risk maximization are the two analytical cases of portfolio optimality taken into consideration. Robust portfolio optimizations, using shrinkage estimations and newly proposed risk-based weight constraints, are also applied. The evidence demonstrates that the portfolio analysis outcomes regarding currency contagions and flights, implying diversification benefits, vary and are noticeably dissimilar from the correlation analysis outcomes of Chapter 1. Subsequently, it could be inferred that the diversification benefits deduced from the portfolio and correlation analyses differ owing to the dominance, during market uncertainty, of the behaviors of the means and (co)variances of all the shock-originating and shock-receiving returns, over the behaviors of just bivariate correlations between the shock-originating and shock-receiving returns. Moreover, corrections of the heteroskedasticity bias inherent in the shock-originating returns, overall, do not have an effect on currency portfolio rebalancing. Additionally, hedging demands could be implied from detected structural portfolio reallocations, probably as a result of variance-covariance shocks rising from Brexit.

<p>Optimization under uncertainty is the field of optimization where the data or the optimization model itself has uncertainties associated with it. Such problems are more commonly referred to as stochastic optimization problems. These problems capture the broad idea of making optimal decisions under uncertainty. An important class of these stochastic optimization problems is chance-constrained optimization problems, where the decision maker seeks to choose the best decision such that the probability of violating a set of uncertainty constraints is within a predefined probabilistic threshold risk level. Such stochastic optimization problems have found a lot of interest in the service industry as the service providers need to satisfy a minimum service level agreement (SLA) with their customers. Satisfying SLA in the presence of uncertainty in the form of probabilistic failure of infrastructure poses many interesting and challenging questions. In this thesis, we answer a few of these questions.</p> <p>We first explore the problem of quantifying uncertainties that adversely impact the service provider's infrastructure, thereby hurting the service level agreements. In particular we address the probability quantification problem, where given an uncertainty set, the goal is to quantify the probability of an event, on which the optimal value of an optimization problem exceeds a predefined threshold value. The novel techniques we propose, use and develop ideas from diverse literatures such as mixed integer nonlinear program, chance-constrained programming, approximate sampling and counting techniques, and large deviation bounds. Our approach yields the first polynomial time approximation scheme for the specific probability quantification problem we consider. </p> <p>Our next work is inspired by the ideas of risk averse decision making. Here, we focus on studying the problem of minimizing risk functions. As a special case we also explore the problem of minimizing the Value at Risk (VaR), which is a well know non-convex problem. For more than a decade, the well-known, best convex approximation to this problem has been obtained by minimizing the Conditional Value at Risk (CVaR). We proposed a new two-stage model which formulates these risk functions, which eventually leads to a bilinear optimization problem, a special case of which is the VaR minimization problem. We come up with enhancements to this bilinear formulation and use convexification techniques to obtain tighter lower and upper convex approximations to the problem. We also find that the approximation obtained by CVaR minimization is a special case of our method. The overestimates we construct help us to develop tighter convex inner approximations for the chance constraint optimization problems.</p>

傳統人壽保險契約之分析利用等價原則(principal of equivalience) 來對商品評價。即保險人所收保費之現值等於保險人未來責任(保險金額給付)之現值。然而對於權益連結壽險商品而言，其結合傳統商品之風險(如利率風險、死亡率風險等)與財務風險，故更增加其評價困難性。過去研究中在假設預定利率為常數與死亡率為給定的情況下，利用Black-Scholes (1973)評價公式推導出公式解。然而Black-Scholes評價公式是建構在完全市場上，對於權益連結壽險商品而言其已不符合完全市場之假設，因此本文放寬完全市場之假設來對此商品重新評價與避險。 在財務市場上，對於不完全市場(incomplete markets)下請求權(contingent claims)之評價與避險，已發展出數個不同評價方法。本文利用均數變異避險(mean-variance hedging)方法(Follmer&Sondermann ，1986)所衍生之風險極小化(risk-minimization)觀念來對此保險衍生性金融商品評價與避險，並找到一風險衡量測度(Moller , 1996、1998a、2000)來評估發行此商品保險人需承受多少風險。 / In this study, actuarial equivalent principle and no-arbitrage pricing theory are used in pricing and valuation for unit-linked life insurance policies.　Since their market values cannot be replicated through the self-finance strategies due to market incompleteness, the theoretical setup in Black and Scholes (1973) and Follmer and Sondermann (1986) are adopted to develop the pricing and hedging strategies. Counting process is employed to characterize the transition pattern of the policyholder and the linked assets are modeled through the geometric Brownian motions. Equivalent martingale measures are adapted to derive the pricing formulas. Since the benefit payments depend on the performance of the underlying portfolios and the health status of the policyholder, mean-variance minimization criterion is employed to evaluate the financial risk. Finally pricing and hedging issues are examined through the numerical illustrations. Monte Carlo method is implemented to approximate the market premiums according to the payoff structures of the policies. In this paper, we show that the risk-minimization criterion can be used to determine the hedging strategies and access the minimal intrinsic risks for the insurers.