We propose a Markov chain model for credit rating changes. We do not use any distributional assumptions on the asset values of the rated companies but directly model the rating transitions process. The parameters of the model are estimated by a maximum likelihood approach using historical rating transitions and heuristic global optimization techniques. We benchmark the model against a GLMM model in the context of bond portfolio risk management. The proposed model yields stronger dependencies and higher risks than the GLMM model. As a result, the risk optimal portfolios are more conservative than the decisions resulting from the benchmark model.

This thesis presents two Models of portfolio optimization, namely the Markowitz Mean Variance Optimization Model and the Rockefeller and Uryasev CVaR Optimization Model. It then presents an application of these models to a portfolio of clean energy assets for optimal allocation of financial resources in terms of maximum returns and low risk. This is done by writing GAMS programs for these optimization problems. An in-depth analysis of the results is conducted, and we see that the difference between both models is not very significant even though these results are data-specific.

Routing and designing are essential for transportation networks. With effective routing and designing policies, transportation networks can work safely and efficiently. There are two transportation problems: hazardous materials (hazmat) transportation and warehouse logistics. This dissertation addresses the routing of networks for both problems. For hazmat transportation, the routing can be regulated via network design. Due to catastrophic consequences of potential accidents in hazmat transportation, a risk-averse approach for routing is necessary. In this dissertation, we consider spectral risk measures, for risk-averse hazmat routing. In addition, we introduce a network design problem to select a set of closed road segments for hazmat traffic with conditional value-at-risk (CVaR) to regulate hazmat routing. In warehouses, the routing of electric forklifts with sufficient battery levels is for material handling. The optimization model of dynamic wireless charging lane location is proposed under the workflow congestion in parallel-aisle warehouses. Considering the uncertainty of demands, the wireless charging lane location problem is formulated as a two-stage stochastic programming model. We confirm the efficiency of the proposed algorithms in solving these problems and the key advantages of use the proposed routing and designing policies via case studies.

This thesis provides an analysis of systemic risk in the US banking sector. We use conditional value at risk (∆CoVaR), marginal expected shortfall (MES) and cross-quantilogram (CQ) to statistically measure tail-dependence in return series of individual institutions and the system as a whole. Wavelet multireso- lution analysis is used to study systemic risk in the time-frequency domain. De- composition of returns on different scales allows us to isolate cycles of 2-8 days, 8-32 days and 32-64 days and analyze co-movement patterns which would oth- erwise stay hidden. Empirical results demonstrate that filtering out short-term noise from the return series improves the forecast power of ∆CoVaR. Eventu- ally, we investigate the connection between statistical measures of systemic risk and fundamental characteristics of institutions (size, leverage, market to book ratio) and conclude that size is the most robust determinant of systemic risk.

This thesis performs portfolio optimization using three allocation methods, Certainty Equivalence Tangency (CET), Global Minimum Variance (GMV) and Minimum Conditional Value-at-Risk (MinCVaR). We estimate expected returns and covariance matrices based on 7 stock market indices with a DCC-GARCH model including an ARMA (1.1) process and an external regressor of an implied volatility index (VIX). We then simulate returns using a rolling window of 500 daily observations and construct portfolios based on the allocation methods. The results suggest that the model can sufficiently estimate expected returns and covariance matrices and we can outperform benchmarks in form of equally weighted and historical portfolios in terms of higher returns and lower risk. Over the whole out-of-sample period the CET portfolio yields the highest mean returns and GMV and MinCVaR can significantly lower the variance. The inclusion of VIX has marginal effects on the forecasting accuracy and it seems to impair the estimation of risk.

Cette thèse est consacrée à des problématiques numériques probabilistes liées à la modélisation, au contrôle et à la gestion du risque et motivées par des applications dans les marchés de l'énergie. Le principal outil utilisé est la théorie des algorithmes stochastiques et des méthodes de simulation. Cette thèse se compose de trois parties. La première est dévouée à l'estimation de deux mesures de risque de la distribution L des pertes d'un portefeuille: la Value-at-Risk (VaR) et la Conditional Value-at-Risk (CVaR). Cette estimation est effectuée à l'aide d'un algorithme stochastique combiné avec une méthode de réduction de variance adaptative. La première partie de ce chapitre traite du cas de la dimension finie, la deuxième étend la première au cas d'une fonction de la trajectoire d'un processus et la dernière traite du cas des suites à discrépance faible. Le deuxième chapitre est dédié à des méthodes de couverture du risque en CVaR dans un marché incomplet opérant à temps discret à l'aide d'algorithmes stochastiques et de quantification vectorielle optimale. Des résultats théoriques sur la couverture en CVaR sont présentés puis les aspects numériques sont abordés dans un cadre markovien. La dernière partie est consacrée à la modélisation conjointe des prix des contrats spot Gaz et l'Electricité. Le modèle multi-facteur présenté repose sur des processus d'Ornstein stationnaires à coefficient de diffusion paramétrique.

In this thesis we mainly focused on the usage of the Conditional Value-at-Risk (CVaR) in risk management and on the pricing of the arithmetic average basket and Asian options in the Black-Scholes framework via a new log-normal sum approximation method. Firstly, we worked on the linearization procedure of the CVaR proposed by Rockafellar and Uryasev. We constructed an optimization problem with the objective of maximizing the expected return under a CVaR constraint. Due to possible intermediate payments we assumed, we had to deal with a re-investment problem which turned the originally one-period problem into a multiperiod one. For solving this multi-period problem, we used the linearization procedure of CVaR and developed an iterative scheme based on linear optimization. Our numerical results obtained from the solution of this problem uncovered some surprising weaknesses of the use of Value-at-Risk (VaR) and CVaR as a risk measure. In the next step, we extended the problem by including the liabilities and the quantile hedging to obtain a reasonable problem construction for managing the liquidity risk. In this problem construction the objective of the investor was assumed to be the maximization of the probability of liquid assets minus liabilities bigger than a threshold level, which is a type of quantile hedging. Since the quantile hedging is not a perfect hedge, a non-zero probability of having a liability value higher than the asset value exists. To control the amount of the probable deficient amount we used a CVaR constraint. In the Black-Scholes framework, the solution of this problem necessitates to deal with the sum of the log-normal distributions. It is known that sum of the log-normal distributions has no closed-form representation. We introduced a new, simple and highly efficient method to approximate the sum of the log-normal distributions using shifted log-normal distributions. The method is based on a limiting approximation of the arithmetic mean by the geometric mean. Using our new approximation method we reduced the quantile hedging problem to a simpler optimization problem. Our new log-normal sum approximation method could also be used to price some options in the Black-Scholes model. With the help of our approximation method we derived closed-form approximation formulas for the prices of the basket and Asian options based on the arithmetic averages. Using our approximation methodology combined with the new analytical pricing formulas for the arithmetic average options, we obtained a very efficient performance for Monte Carlo pricing in a control variate setting. Our numerical results show that our control variate method outperforms the well-known methods from the literature in some cases.

Sample average approximation (SAA) is a well-known solution methodology for traditional stochastic programs which are risk neutral in the sense that they consider optimization of expectation functionals. In this thesis we establish sample average approximation methods for two classes of non-traditional stochastic programs. The first class is that of stochastic min-max programs, i.e., min-max problems with expected value objectives, and the second class is that of expected value constrained stochastic programs. We specialize these SAA methods for risk-averse stochastic problems with a bi-criteria objective involving mean and mean absolute deviation, and those with constraints on conditional value-at-risk. For the proposed SAA methods, we prove that the results of the SAA problem converge exponentially fast to their counterparts for the true problem as the sample size increases. We also propose implementation schemes which return not only candidate solutions but also statistical upper and lower bound estimates on the optimal value of the true problem. We apply the proposed methods to solve portfolio selection and supply chain network design problems. Our computational results reflect good performance of the proposed SAA schemes. We also investigate the effect of various types of risk-averse stochastic programming models in controlling risk in these problems.

Il est prévu que la génération distribuée par l’entremise d’énergie de sources renouvelables (DG) continuera à jouer un rôle clé dans le développement et l’exploitation des systèmes de puissance électrique durables, efficaces et fiables, en vertu de cette fournit une alternative pratique de décentralisation et diversification de la demande globale d’énergie, bénéficiant de sources d’énergie plus propres et plus sûrs. L’intégration de DG renouvelable dans les réseaux électriques existants pose des défis socio–technico–économiques, qu’ont attirés de la recherche et de progrès substantiels.Dans ce contexte, la présente thèse a pour objet la conception et le développement d’un cadre de modélisation, simulation et optimisation pour l’intégration de DG renouvelable dans des réseaux de puissance électrique existants. Le problème spécifique à considérer est celui de la sélection de la technologie,la taille et l’emplacement de des unités de génération renouvelable d’énergie, sous des contraintes techniques, opérationnelles et économiques. Dans ce problème, les questions de recherche clés à aborder sont: (i) la représentation et le traitement des variables physiques incertains (comme la disponibilité de les diverses sources primaires d’énergie renouvelables, l’approvisionnement d’électricité en vrac, la demande de puissance et l’apparition de défaillances de composants) qui déterminent dynamiquement l’exploitation du réseau DG–intégré, (ii) la propagation de ces incertitudes sur la réponse opérationnelle du système et le suivi du risque associé et (iii) les efforts de calcul intensif résultant du problème complexe d’optimisation combinatoire associé à l’intégration de DG renouvelable.Pour l’évaluation du système avec un plan d’intégration de DG renouvelable donné, un modèle de calcul de simulation Monte Carlo non–séquentielle et des flux de puissance optimale (MCS–OPF) a été conçu et mis en oeuvre, et qui émule l’exploitation du réseau DG–intégré. Réalisations aléatoires de scénarios opérationnels sont générés par échantillonnage à partir des différentes distributions des variables incertaines, et pour chaque scénario, la performance du système est évaluée en termes économiques et de la fiabilité de l’approvisionnement en électricité, représenté par le coût global (CG) et l’énergie non fournie (ENS), respectivement. Pour mesurer et contrôler le risque par rapport à la performance du système, deux indicateurs sont introduits, la valeur–à–risque conditionnelle(CVaR) et l’écart du CVaR (DCVaR).Pour la sélection optimale de la technologie, la taille et l’emplacement des unités DG renouvelables,deux approches distinctes d’optimisation multi–objectif (MOO) ont été mis en oeuvre par moteurs de recherche d’heuristique d’optimisation (HO). La première approche est basée sur l’algorithme génétique élitiste de tri non-dominé (NSGA–II) et vise à la réduction concomitante de l’espérance mathématique de CG et de ENS, dénotés ECG et EENS, respectivement, combiné avec leur valeurs correspondent de CVaR(CG) et CVaR(ENS); la seconde approche effectue un recherche à évolution différentielle MOO (DE) pour minimiser simultanément ECG et s’écart associé DCVaR(CG). Les deux approches d’optimisation intègrent la modèle de calcul MCS–OPF pour évaluer la performance de chaque réseau DG–intégré proposé par le moteur de recherche HO.Le défi provenant de les grands efforts de calcul requises par les cadres de simulation et d’optimisation proposée a été abordée par l’introduction d’une technique originale, qui niche l’analyse de classification hiérarchique (HCA) dans un moteur de recherche de DE.Exemples d’application des cadres proposés ont été élaborés, concernant une adaptation duréseau test de distribution électrique IEEE 13–noeuds et un cadre réaliste du système test de sous–transmission et de distribution IEEE 30–noeuds. [...] / Renewable distributed generation (DG) is expected to continue playing a fundamental role in the development and operation of sustainable, efficient and reliable electric power systems, by virtue of offering a practical alternative to diversify and decentralize the overall power generation, benefiting from cleaner and safer energy sources. The integration of renewable DG in the existing electric powernetworks poses socio–techno–economical challenges, which have attracted substantial research and advancement.In this context, the focus of the present thesis is the design and development of a modeling,simulation and optimization framework for the integration of renewable DG into electric powernetworks. The specific problem considered is that of selecting the technology, size and location of renewable generation units, under technical, operational and economic constraints. Within this problem, key research questions to be addressed are: (i) the representation and treatment of the uncertain physical variables (like the availability of diverse primary renewable energy sources, bulk–power supply, power demands and occurrence of components failures) that dynamically determine the DG–integrated network operation, (ii) the propagation of these uncertainties onto the system operational response and the control of the associated risk and (iii) the intensive computational efforts resulting from the complex combinatorial optimization problem of renewable DG integration.For the evaluation of the system with a given plan of renewable DG, a non–sequential MonteCarlo simulation and optimal power flow (MCS–OPF) computational model has been designed and implemented, that emulates the DG–integrated network operation. Random realizations of operational scenarios are generated by sampling from the different uncertain variables distributions,and for each scenario the system performance is evaluated in terms of economics and reliability of power supply, represented by the global cost (CG) and the energy not supplied (ENS), respectively.To measure and control the risk relative to system performance, two indicators are introduced, the conditional value–at–risk (CVaR) and the CVaR deviation (DCVaR).For the optimal technology selection, size and location of the renewable DG units, two distinct multi–objective optimization (MOO) approaches have been implemented by heuristic optimization(HO) search engines. The first approach is based on the fast non–dominated sorting genetic algorithm(NSGA–II) and aims at the concurrent minimization of the expected values of CG and ENS, thenECG and EENS, respectively, combined with their corresponding CVaR(CG) and CVaR(ENS) values; the second approach carries out a MOO differential evolution (DE) search to minimize simultaneously ECG and its associated deviation DCVaR(CG). Both optimization approaches embed the MCS–OPF computational model to evaluate the performance of each DG–integrated network proposed by the HO search engine. The challenge coming from the large computational efforts required by the proposed simulation and optimization frameworks has been addressed introducing an original technique, which nests hierarchical clustering analysis (HCA) within a DE search engine. Examples of application of the proposed frameworks have been worked out, regarding an adaptation of the IEEE 13 bus distribution test feeder and a realistic setting of the IEEE 30 bussub–transmission and distribution test system. The results show that these frameworks are effectivein finding optimal DG–integrated networks solutions, while controlling risk from two distinctperspectives: directly through the use of CVaR and indirectly by targeting uncertainty in the form ofDCVaR. Moreover, CVaR acts as an enabler of trade–offs between optimal expected performanceand risk, and DCVaR integrates also uncertainty into the analysis, providing a wider spectrum ofinformation for well–supported and confident decision making.

The thesis presents test statistics of Value-at-Risk and Conditional Value-at-Risk. The reader is familiar with basic nonparametric estimators and their asymptotic distributions. Tests of accuracy of Value-at- Risk are explained and asymptotic test of Conditional Value-at-Risk is derived. The thesis is concluded by process of backtesting of Value-at-Risk model using real data and computing statistical power and probability of Type I error for selected tests. Powered by TCPDF (www.tcpdf.org)