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.

L'objectif de cette thèse consiste à présenter un nouvel algorithme pour la programmation non linéaire en nombres entiers, inspirée par la méthode Multiplicative Weights Update et qui compte sur une nouvelle classe de reformulations, appelées les reformulations ponctuelles.La programmation non linéaire en nombres entiers est un sujet très difficile et fascinant dans le domaine de l'optimisation mathématique à la fois d'un point de vue théorique et computationnel. Il est possible de formuler de nombreux problèmes dans ce schéma général et, habituellement, ils posent de réels défis en termes d'efficacité et de précision de la solution obtenue quant aux procédures de résolution.La thèse est divisée en trois parties principales : une introduction composée par le Chapitre 1, une définition théorique du nouvel algorithme dans le Chapitre 2 et l'application de cette nouvelle méthodologie à deux problèmes concrets d'optimisation, tels que la sélection optimale du portefeuille avec le critère moyenne-variance dans le Chapitre 3 et le problème du sac à dos non linéaire dans le Chapitre 4. Conclusions et questions ouvertes sont présentées dans le Chapitre 5. / This thesis presents a new algorithm for Mixed Integer NonLinear Programming, inspired by the Multiplicative Weights Update framework and relying on a new class of reformulations, called the pointwise reformulations.Mixed Integer NonLinear Programming is a hard and fascinating topic in Mathematical Optimization both from a theoretical and a computational viewpoint. Many real-word problems can be cast this general scheme and, usually, are quite challenging in terms of efficiency and solution accuracy with respect to the solving procedures.The thesis is divided in three main parts: a foreword consisting in Chapter 1, a theoretical foundation of the new algorithm in Chapter 2, and the application of this new methodology to two real-world optimization problems, namely the Mean-Variance Portfolio Selection in Chapter 3, and the Multiple NonLinear Separable Knapsack Problem in Chapter 4. Conclusions and open questions are drawn in Chapter 5.