In this thesis, several Reliability-based Design Optimization (RBDO) methods and algorithms for airplane floor grid layout optimization are proposed. A general RBDO process is proposed and validated by an example. Copula as a mathematical method to model random variable correlations is introduced to discover the correlations between random variables and to be applied in producing correlated data samples for Monte Carlo simulations. Based on Hasofer-Lind (HL) method, a correlated HL method is proposed to evaluate a reliability index under correlation. As an alternative method for computing a reliability index, the reliability index is interpreted as an optimization problem and two nonlinear programming algorithms are introduced to evaluate reliability index. To evaluate the reliability index by Monte Carlo simulation in a time efficient way, a kriging-based surrogate model is proposed and compared to the original model in terms of computing time. Since in RBDO optimization models the reliability constraint obtained by MCS does not have an analytical form, a kriging-based response surface is built. Kriging-based response surface models are usually segment functions that do not have a uniform expression over the design space; however, most optimization algorithms require a uniform expression for constraints. To solve this problem, a heuristic gradient-based direct searching algorithm is proposed. These methods and algorithms, together with the RBDO general process, are applied to the layout optimization of aircraft floor grid structural design.

The main objective of this thesis is to develop novel Monte Carlo techniques with emphasis on various applications in finance and economics, particularly in the fields of risk management and asset returns modeling. New stochastic algorithms are developed for rare-event probability estimation, combinatorial optimization, parameter estimation and model selection. The contributions of this thesis are fourfold. Firstly, we study an NP-hard combinatorial optimization problem, the Winner Determination Problem (WDP) in combinatorial auctions, where buyers can bid on bundles of items rather than bidding on them sequentially. We present two randomized algorithms, namely, the cross-entropy (CE) method and the ADAptive Mulitilevel splitting (ADAM) algorithm, to solve two versions of the WDP. Although an efficient deterministic algorithm has been developed for one version of the WDP, it is not applicable for the other version considered. In addition, the proposed algorithms are straightforward and easy to program, and do not require specialized software. Secondly, two major applications of conditional Monte Carlo for estimating rare-event probabilities are presented: a complex bridge network reliability model and several generalizations of the widely popular normal copula model used in managing portfolio credit risk. We show how certain efficient conditional Monte Carlo estimators developed for simple settings can be extended to handle complex models involving hundreds or thousands of random variables. In particular, by utilizing an asymptotic description on how the rare event occurs, we derive algorithms that are not only easy to implement, but also compare favorably to existing estimators. Thirdly, we make a contribution at the methodological front by proposing an improvement of the standard CE method for estimation. The improved method is relevant, as recent research has shown that in some high-dimensional settings the likelihood ratio degeneracy problem becomes severe and the importance sampling estimator obtained from the CE algorithm becomes unreliable. In contrast, the performance of the improved variant does not deteriorate as the dimension of the problem increases. Its utility is demonstrated via a high-dimensional estimation problem in risk management, namely, a recently proposed t-copula model for credit risk. We show that even in this high-dimensional model that involves hundreds of random variables, the proposed method performs remarkably well, and compares favorably to existing importance sampling estimators. Furthermore, the improved CE algorithm is then applied to estimating the marginal likelihood, a quantity that is fundamental in Bayesian model comparison and Bayesian model averaging. We present two empirical examples to demonstrate the proposed approach. The first example involves women's labor market participation and we compare three different binary response models in order to find the one best fits the data. The second example utilizes two vector autoregressive (VAR) models to analyze the interdependence and structural stability of four U.S. macroeconomic time series: GDP growth, unemployment rate, interest rate, and inflation. Lastly, we contribute to the growing literature of asset returns modeling by proposing several novel models that explicitly take into account various recent findings in the empirical finance literature. Specifically, two classes of stylized facts are particularly important. The first set is concerned with the marginal distributions of asset returns. One prominent feature of asset returns is that the tails of their distributions are heavier than those of the normal---large returns (in absolute value) occur much more frequently than one might expect from a normally distributed random variable. Another robust empirical feature of asset returns is skewness, where the tails of the distributions are not symmetric---losses are observed more frequently than large gains. The second set of stylized facts is concerned with the dependence structure among asset returns. Recent empirical studies have cast doubts on the adequacy of the linear dependence structure implied by the multivariate normal specification. For example, data from various asset markets, including equities, currencies and commodities markets, indicate the presence of extreme co-movement in asset returns, and this observation is again incompatible with the usual assumption that asset returns are jointly normally distributed. In light of the aforementioned empirical findings, we consider various novel models that generalize the usual normal specification. We develop efficient Markov chain Monte Carlo (MCMC) algorithms to estimate the proposed models. Moreover, since the number of plausible models is large, we perform a formal Bayesian model comparison to determine the model that best fits the data. In this way, we can directly compare the two approaches of modeling asset returns: copula models and the joint modeling of returns.

This thesis investigates an exclamative construction very used by the native speakers of Brazilian Portuguese, but under-researched, namely, the Free Small Clauses (FSCs), juxtaposition of a predicate and its subject, in that order, without any verb or morphological specification for tense on the surface, as in the following construction Bonita a sua roupa Your Clothes are beautiful , for example. The main goal of this study is to answer the following question: what is the internal structure of the FSCs of Brazilian Portuguese? In order to answer this question, at first, this work establishes what are the syntactic-semantic restrictions which govern the constitutive elements of this kind of constructions, describing the contexts in which the predicate and the subject can act. For the analysis of FSCs, we took as the theoretical assumptions the generative enterprise in its minimalist model (cf. CHOMSKY, 2000 et passim), as well as the notion of predication and phase extension as delimited in Den Dikken (2006, 2007). To answer the question put before, i.e., what is the internal structure of FSCs, we did several tests to understand what would be the internal composition of this type of structure and what is the structural position of its elements. What we could conclude in the end of this work is that the FSCs are root TPs, that is, one TP phase. Differently of Chomsky (2000), who admits that only CP and v*P can be strong phases, this thesis bring some evidences from Brazilian Portuguese in favor of the idea that TP would also be a phase. / Conselho Nacional de Desenvolvimento Científico e Tecnológico / Esta tese investiga uma construção exclamativa muito usada pelos falantes do português brasileiro, mas pouco estudada, nomeadamente, as Small Clauses Livres (SCLs), a justaposição de um predicado e seu sujeito, nessa ordem, sem nenhum verbo nem nenhuma informação de tempo na superfície, como na construção Bonita a sua roupa, por exemplo. O principal objetivo deste estudo é responder a seguinte questão: qual a estrutura interna das SCLs do Português Brasileiro? Para tal investigação, o presente trabalho, num primeiro momento, estabelece quais são as restrições sintático-semânticas que regem os elementos constitutivos desse tipo de construção, descrevendo os contextos em que o predicado e o sujeito podem atuar. Para a análise das SCLs, tomamos como embasamento teórico os pressupostos da Teoria Gerativa no seu modelo minimalista (cf. CHOMSKY, 2000 e seqüência), bem como a noção de predicação e extensão de fase de Den Dikken (2006, 2007). A fim de desvendar qual a estrutura interna das SCLs, fizemos diversos testes no sentido de entender qual seria a composição interna desse tipo de estrutura e qual a posição estrutural de seus elementos. O que esta pesquisa conclui é que as SCLs são TPs raízes, ou seja, uma fase TP, desse modo, diferentemente de Chomsky (2000), que admite apenas CP e v*P como uma fase forte, esta tese traz evidências a favor da idéia TP também seria uma fase.

Made available in DSpace on 2010-04-20T21:00:11Z (GMT). No. of bitstreams: 4 Mauricio Mussashi Irie.pdf.jpg: 16022 bytes, checksum: d3dcf1b8020749a12b3baae53334cda5 (MD5) Mauricio Mussashi Irie.pdf.txt: 96735 bytes, checksum: 944036c3b3d1ae823db79daedb65dd6e (MD5) Mauricio Mussashi Irie.pdf: 7355110 bytes, checksum: 880246debd0d864c44768ebd4eaf2e6e (MD5) license.txt: 4886 bytes, checksum: 8fa2d810f5b64e058d76fb4986924cf0 (MD5) Previous issue date: 2009-02-06T00:00:00Z / Este trabalho explora com cuidado o lado específico da implementação de um modelo de alocação de ativos em que o risco é tratado de maneira integrada, não somente através do desvio padrão do portfólio, mas também considerando outras métricas de risco como, por exemplo, o Expected Shortfall. Além disso, utilizamos algumas técnicas de como trabalhar com as variáveis de modo a extrair do mercado os chamados "invariantes de mercado", fenômenos que se repetem e podem ser modelados como variáveis aleatórias independentes e identicamente distribuídas. Utilizamos as distribuições empíricas dos invariantes, juntamente com o método de Cópulas para gerar um conjunto de cenários multivariados simulados de preços. Esses cenários são independentes de distribuição, portanto são não paramétricos. Através dos mesmos, avaliamos a distribuição de retornos simulados de um portfólio através de um índice de satisfação que é baseado em uma função de utilidade quadrática e utiliza o Expected Shortfall como métrica de risco. O índice de satisfação incorpora o trade-off do investidor entre risco e retorno. Finalmente, escolhemos como alocação ótima aquela que maximiza o índice de satisfação ajustado a um parâmetro de aversão ao risco. Perseguindo esses passos, é possível obter um portfólio no qual a alocação em cada ativo, ou classe de ativos, reflete o prêmio esperado ao risco incorrido. / The present work carefully explores the implementation of an asset allocation model in which the risk measure considered is fully integrated, not only through the standard deviation for the portfolio, but also considering other risk metrics, for instance, the Expected Shortfall. Moreover, some statistical tools are used to extract from the market the so called “market invariants”, which are phenomena that tend to repeat themselves and can be modeled as i.i.d. random variables. We use the empirical distribution of the invariants, along with the Method of Copula to generate a set of simulated multivariate price scenarios. These scenarios are independent of distribution, therefore they are non-parametric. With these scenarios we evaluate the simulated return distribution of a portfolio through a satisfaction index which is based on a quadratic utility function and the risk measure considered is the Expected Shortfall. The satisfaction index summarizes the investor trade-off between risk and return. Finally, we choose the optimal allocation that maximizes the satisfaction index adjusted to a risk aversion parameter. In pursuing these steps, it is possible to obtain a portfolio in which the allocation of each asset class or security fully reflects the expected premium to the risk assumed.

[pt] Nesta dissertação avalia-se o grau de associação entre pares de excessos de retornos, simultâneos e defasados no tempo, usando-se o conceito de cópulas. Cópulas assimétricas são ajustadas aos pares de distribuições de retornos e coeficientes de dependência de cauda, as medidas de interdependência e contágio baseadas nessas cópulas, são calculados para 10 pares de índices de mercados. Tais coeficientes balizam a escolha do par de ativos com melhor desempenho em períodos de estresse. Se excessos defasados são incluídos, então estes coeficientes também indicam a direção e intensidade de propagação das crises (contágio). Os resultados encontrados na nossa investigação mostram que a técnica utilizada é eficaz na montagem de carteiras em que se pretende aproveitar os ganhos extremos conjuntos dos ativos e, ao mesmo tempo, evitar perdas extremas conjuntas. O uso de retornos defasados, porém, foi um artifício pouco producente, refletindo possivelmente o contágio quase instantâneo entre os mercados financeiros mundiais, nos dias de hoje. / [en] In this dissertation we evaluate the degree of association between pairs of excess of returns, simultaneous and lagged, using the concept of copulas. Asymmetric copulas are fitted to 10 pairs of distributions of returns of world markets índices. From these copulas coefficients of tail dependence are obtained for the right and left tails. Isong those coefficients as measures of cross dependence and contagion between markets one can pick the pair of returns that show the best performance in periods of stress. If lagged excess of returns are included, then these coefficients provide information on the direction and intensity of the contagion spread. Our results have shown that such technique isd efficent in constructing a portfolio in which one wants to take advantage of joint extreme gains of pairs of returns and, simultaneously, avoid losses associated with the occurrence of joint negative extremes. The use of lagged returns in this context hás shown no extra gain, maybe reflecting the fact that, nowadays, the spread of contagion between world financial markets is almost instantaneous.

Neste trabalho são apresentados modelos de regressão com respostas bivariadas obtidos através de funções cópulas. O objetivo de utilizar estes modelos bivariados é modelar a correlação entre eventos e captar nos modelos de regressão a influência da associação entre as variáveis resposta na presença de censura nos dados. Os parâmetros dos modelos, são estimados por meio dos métodos de máxima verossimilhança e jackknife. Alguns métodos de análise de sensibilidade como influência global, local e local total de um indivíduo, são introduzidos e calculados considerando diferentes esquemas de perturbação. Uma análise de resíduos foi proposta para verificar a qualidade do ajuste dos modelos utilizados e também foi proposta novas medidas de resíduos para respostas bivariadas. Métodos de simulação de Monte Carlo foram conduzidos para estudar a distribuição empírica dos resíduos marginais e bivariados propostos. Finalmente, os resultados são aplicados à dois conjuntos de dados dsponíveis na literatura. / In this work bivariate response regression models are presented with the use of copulas. The objective of this approach is to model the correlation between events and capture the influence of this correlation in the regression parameters. The models are used in the context of survival analysis and are ¯tted to two data sets available in the literature. Inferences are obtained using maximum likelihood and Jackknife methods. Sensitivity techniques such as local and global in°uence are proposed and calculated. A residual analysis is proposed to check the adequacy of the models and simulation methods are used to asses the empirical distribution of the marginal univariate and bivariate residual measures proposed.

Orientador: Luiz Koodi Hotta / Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Cientifica / Made available in DSpace on 2018-08-12T14:00:24Z (GMT). No. of bitstreams: 1 Busato_ErickAndrade_M.pdf: 4413458 bytes, checksum: b9c4c39b4639c19e685bae736fc86c4f (MD5) Previous issue date: 2008 / Resumo: A família de distribuições t-Student Assimétrica, construída a partir da mistura em média e variância da distribuição normal multivariada com a distribuição Inversa Gama possui propriedades desejáveis de flexibilidade para as mais diversas formas de assimetria. Essas propriedades são exploradas na construção de funções de acoplamento que possuem dependência assimétrica. Neste trabalho são estudadas as características e propriedades da distribuição t-Student Assimétrica e a construção da respectiva função de acoplamento, fazendo-se uma apresentação de diferentes estruturas de dependência que pode originar, incluindo assimetrias da dependência nas caudas. São apresentados métodos de estimação de parâmetros das funções de acoplamento, com aplicações até a terceira dimensão da cópula. Essa função de acoplamento é utilizada para compor um modelo ARMA-GARCHCópula com marginais de distribuição t-Student Assimétrica, que será ajustado para os logretornos de preços do Petróleo e da Gasolina, e log-retornos do Índice de Óleo AMEX, buscando o melhor ajuste, principalmente, para a dependência nas caudas das distribuições de preços. Esse modelo será comparado, através de medidas de Valor em Risco e AIC, além de outras medidas de bondade de ajuste, com o modelo de Função de Acoplamento t-Student Simétrico. / Abstract: The Skewed t-Student distribution family, constructed upon the multivariate normal mixture distribution, known as mean-variance mixture, composed with the Inverse-Gamma distribution, has many desirable flexibility properties for many distribution asymmetry structures. These properties are explored by constructing copula functions with asymmetric dependence. In this work the properties and characteristics of the Skewed t-Student distribution and the construction of a respective copula function are studied, presenting different dependence structures that the copula function generates, including tail dependence asymmetry. Parameter estimation methods are presented for the copula, with applications up to the 3rd dimension. This copula function is used to compose an ARMAGARCH- Copula model with Skewed t-Student marginal distribution that is adjusted to logreturns of Petroleum and Gasoline prices and log-returns of the AMEX Oil Index, emphasizing the return's tail distribution. The model will be compared, by the means of the VaR (Value at Risk) and Akaike's Information Criterion, along with other Goodness-of-fit measures, with models based on the Symmetric t-Student Copula. / Mestrado / Mestre em Estatística

Cette thèse établit un cadre d’évaluation des stress tests financiers, en identifiant leurs principales limites. Trois approches ont été proposées pour améliorer les pratiques actuelles à chaque étape du processus. Elles incluent : (i) un modèle semi-paramétrique TVE–copules-paires pour les facteurs de risque financiers, avec un accent particulier sur les valeurs extrêmes, (ii) un modèle d'évaluation pour estimer l'impact de ces facteurs sur un système financier, via des effets directs, indirects et de contagion, en considérant les réactions endogènes publiques et privées, et (iii) une approche bayésienne pour mener une sélection systématique des scénarios de stress pour des portefeuilles non linéaires. Le modèle de risque a montré de meilleures performances par rapport à la plupart des spécifications courantes ; ce qui augmente la crédibilité du test. Le modèle d'évaluation est estimé pour le système bancaire français, révélant ses principales sources de vulnérabilité et le rôle clé des réactions publiques. Enfin, l'approche bayésienne a permis de remplacer les scénarios subjectifs traditionnels et d’inclure les résultats de stress tests dans la gestion quantitative des risques aux côtés des autres outils conventionnels / This thesis has set a comprehensive framework to assess the relevance of financial stress tests, identifying their main drawbacks. Three robust and flexible model frameworks have been proposed to improve current practices in each of the tests’ stages. This is achieved through: (i) a semi-parametric EVT–Pair-copulas model for financial risk factors, with a specific focus on extreme values, (ii) a valuation model to assess the impact of risk factors on a financial system, through direct and indirect effects, contagion channels, and considering private and public response functions, and (iii) a Bayesian-based approach to run a systematic selection of stress scenarios for nonlinear portfolios. The presented risk model has proven to outperform commonly used specifications, hence increasing the test’s credibility. Estimated for the French banking system, the valuation model revealed the related risk profile and the main vulnerabilities. Public responses turned to be of vital interest. Finally, the Bayesian approach allows replacing the traditional subjective scenarios and including the tests’ results in quantitative risk management alongside with other conventional tools

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / The present work aims to analyze the market risk management copula-GARCH model approach efficiency. To that we use data referent to daily prices of North American, German, Australian, Brazilian, Hong Kong and South African markets, considering the period from July 2002 to June 2012, totalizing ten years of observations. Results allow to conclude that there are volatility clusters along series during sub-prime and Eurozone debt crises. Developed markets present lower general oscillation levels than emerging ones. There was gradual increment in analyzed markets pair to pair dynamic correlation levels, with general levels between 0.3 and 0.6. Computed dynamic VaRs followed returns evolution, not exceeding the expect number of violations, unlike static VaR estimates. Developed markets present rising on optimal hedge ratios starting on sub-prime crisis, while for emerging markets many ratios maintain at same levels. Static ratios did not follow markets evolution. It is identified predominance of the Student t copula on risk and return relationships. However it is not possible to infer existence of an explicit association. Structural change tests indicated breaks in volatility at sub-prime crisis begin, while for correlations there is not homogeneity for breaks or dates. There are patterns on participations which are not followed by markets composed portfolio static weights. During all sample period the dynamic portfolio volatility was less than static one, especially in turbulent periods, with reductions up to 50%. Tests reveal that volatility obtained with Copula-GARCH based strategy is less than those referent to static and dynamic DCC-GARCH approaches. / O presente trabalho visa analisar a eficiência da abordagem de gestão de risco de mercado baseada no modelo Cópula-GARCH. Para tanto são usados dados referentes às cotações diárias dos mercados Norte Americano, Alemão, Australiano, Brasileiro, Honconguês e Sul Africano, considerando o período referente à Julho de 2002 até Junho de 2012, totalizando dez anos de observações. Os resultados permitem concluir que existem agrupamentos de volatilidade ao longo das séries durante as crises do sub-prime e da dívida Europeia. Mercados desenvolvidos apresentam menores níveis gerais de oscilação do que emergentes. Houve incremento gradual no nível de correlação dinâmica par a par dos mercados analisados, com níveis gerais entre 0,3 e 0,6. VaRs dinâmicos computados acompanharam a evolução dos retornos, não excedendo o número esperado de violações, ao contrário das estimativas de VaR estáticas. Mercados desenvolvidos apresentam aumento na razão ótima de hedge a partir da crise do sub-prime, enquanto para os mercados emergentes muitas razões ótimas mantiveram-se nos mesmos patamares. Razões estáticas não acompanharam a evolução dos mercados. É identificado predomínio da cópula t de Student no relacionamento entre risco e retorno. Todavia não é possível inferir a existência de uma associação explícita. Os testes de mudança estrutural indicaram quebras nas volatilidades no início da crise do sub-prime, enquanto para correlações não há homogeneidade de quebras nem de datas. Existem padrões nas participações que não são acompanhadas pelos pesos estáticos dos ativos na composição da carteira construída. Durante todo o período amostral a volatilidade do portfolio dinâmico foi menor que a do estático, especialmente em períodos de maior turbulência, com reduções de até 50%. Testes revelam que a volatilidade obtida com estratégia baseada no modelo Cópula-GARCH é menor que aquelas referentes às abordagens estática e dinâmica efetuada através do modelo DCC-GARCH.

Les études observationnelles (non-randomisées) sont principalement constituées de données ayant des particularités qui sont en fait contraignantes dans un cadre statistique classique. En effet, dans ce type d'études, les données sont rarement continues, complètes et indépendantes du bras thérapeutique dans lequel les observations se situent. Cette thèse aborde l'utilisation d'un outil statistique paramétrique fondé sur la dépendance entre les données à travers plusieurs scénarios liés aux études observationnelles. En effet, grâce au théorème de Sklar (1959), les copules paramétriques sont devenues un sujet d'actualité en biostatistique. Pour commencer, nous présentons les concepts de base relatifs aux copules et aux principales mesures d'association basées sur la concordance retrouvées dans la littérature. Ensuite, nous donnons trois exemples d'application des modèles de copules paramétriques pour autant de cas de données particulières retrouvées dans des études observationnelles. Nous proposons d’abord une stratégie de modélisation de l'analyse coût-efficacité basée uniquement sur une réécriture des fonctions de distribution jointes et évitant les modèles de régression linéaire. Nous étudions ensuite, les contraintes relatives aux données discrètes, particulièrement dans un contexte de non-unicité de la fonction copule, nous réécrivons le score de propension grâce à une approche novatrice basée sur l'extension d'une sous-copule. Enfin, nous évoquons un type particulier de données manquantes : les données censurées à droite, dans un contexte de régression, grâce à l'utilisation de copules semi-paramétriques. / Observational studies (non-randomized) consist primarily of data with features that are in fact constraining within a classical statistical framework. Indeed, in this type of study, data are rarely continuous, complete, and independent of the therapeutic arm the observations are belonging to. This thesis deals with the use of a parametric statistical tool based on the dependence between the data, using several scenarios related to observational studies. Indeed, thanks to the theorem of Sklar (1959), parametric copulas have become a topic of interest in biostatistics. To begin with, we present the basic concepts of copulas, as well as the main measures of association based on the concordance founded on an analysis of the literature. Then, we give three examples of application of models of parametric copulas for as many cases of specific data found in observational studies. We first propose a strategy of modeling cost-effectiveness analysis based essentially on rewriting the joint distribution functions, while discarding the use of linear regression models. We then study the constraints relative to discrete data, particularly in a context of non-unicity of the copula function. We rewrite the propensity score, thanks to an innovative approach based on the extension of a sub-copula. Finally, we introduce a particular type of missing data: right censored data, in a regression context, through the use of semi-parametric copulas.