Financial market and its various components are currently in turmoil. Many large corporations are devising new ways to overcome the current market instability. Consequently, any study fostering the understanding of financial markets and the dependencies of various market components would greatly benefit both the practitioners and academicians. To understand different parts of the financial market, this dissertation employs time series methods to model causality and structure and degree of dependence. The relationship of housing market prices for nine U.S. census divisions is studied in the first essay. The results show that housing market is very interrelated. The New England and West North Central census divisions strongly lead house prices of the rest of the country. Further evidence suggests that house prices of most census divisions are mainly influenced by house price changes of other regions. The interdependence of oil prices and stock market indices across countries is examined in the second essay. The general dependence structure and degree is estimated using copula functions. The findings show weak dependence between stock market indices and oil prices for most countries except for the large oil producing nations which show high dependence. The dependence structure for most oil consuming (producing) countries is asymmetric implying that stock market index and oil price returns tend to move together more during the market downturn (upturn) than a market boom (downturn). In the third essay, the relationship among stock returns of ten U.S. sectors is studied. Copula models are used to explore the non-linear, general association among the series. The evidence shows that sectors are strongly related to each other. Energy sector is relatively weakly connected with the other sectors. The strongest dependence is between the Industrials and Consumer Discretionary sectors. The high dependence suggests small (if any) gains from industry diversification in U.S. In conclusion, the correct formulation of relationships among variables of interest is crucial. This is one of the fundamental issues in portfolio analysis. Hence, a thorough examination of time series models that are used to understand interactions of financial markets can be helpful for devising more accurate investment strategies.

Valuation of R&D projects is quite complex due to the substantial uncertainties in a project's life-cycle phases. The sequential nature of R&D projects continuously provides decision-makers with choices regarding whether and when to undertake future potential investment opportunities. This means that when valuing R&D projects decision-makers should take these factors into account. But R&D project usually takes long time to complete processes for commercialization. If the time to complete is longer, it is easier to trigger the crisis for capital shortage. So it seems very important modeling the capital shortage risk to induce the probability of failure in the pricing model. In this thesis we try to apply the analogy of financial securities subject to credit risk of Jarrow & Turnbull (1995) and attempt to value patents with capital shortage risk in an arbitrage free environment using the martingale measure technique. Furthermore, derive closed form formula for patents valuation which makes application easier than that of the theoretic option model. The major findings are: (1) when considering the effect of the failure frequency (capital shortage risk), the patent value will grow rapidly and then converge in the short run, no matter how other parameters incorporated into the robust analysis; (2) when increasing in the volatility of market revenues with synchronized higher volatility of investment cost, the volatility curve will be distorted to be U-shaped. Meanwhile, lower failure frequency could aggravate the decreasing in the option value. Another issue is when the manager exercises the project with multiple underlying assets, where the assets returns are of non-linear correlation particularly in the non-Normal environment. Non-parametric dependence measures may better employed when explaining co-movement. We focus on the value of a (such as resources development) project in general depends on the price of the multiple products; these are usually correlated to some extent. So the project was treated as having a rainbow option, whose underlying asset prices correlate with each other, and also as having uncertainties that decrease according to the project stage. Based on Cherubini and Luciano’s framework (2002), the risk-neutral copula models are derived to figure decision flexibilities out easily. The main framework studies the valuation of a project (call on Max) by determining the joint risk-neutral distribution of the underlying assets (products) using copulas. Monte-Carlo simulations show that the higher default risk and association among the assets and the expected cost to completion contributes the higher risk premium in our model with dependence structure of Archimedean copula family than traditional Black-Scholes environment. / Valuation of R&D projects is quite complex due to the substantial uncertainties in a project's life-cycle phases. The sequential nature of R&D projects continuously provides decision-makers with choices regarding whether and when to undertake future potential investment opportunities. This means that when valuing R&D projects decision-makers should take these factors into account. But R&D project usually takes long time to complete processes for commercialization. If the time to complete is longer, it is easier to trigger the crisis for capital shortage. So it seems very important modeling the capital shortage risk to induce the probability of failure in the pricing model. In this thesis we try to apply the analogy of financial securities subject to credit risk of Jarrow & Turnbull (1995) and attempt to value patents with capital shortage risk in an arbitrage free environment using the martingale measure technique. Furthermore, derive closed form formula for patents valuation which makes application easier than that of the theoretic option model. The major findings are: (1) when considering the effect of the failure frequency (capital shortage risk), the patent value will grow rapidly and then converge in the short run, no matter how other parameters incorporated into the robust analysis; (2) when increasing in the volatility of market revenues with synchronized higher volatility of investment cost, the volatility curve will be distorted to be U-shaped. Meanwhile, lower failure frequency could aggravate the decreasing in the option value. Another issue is when the manager exercises the project with multiple underlying assets, where the assets returns are of non-linear correlation particularly in the non-Normal environment. Non-parametric dependence measures may better employed when explaining co-movement. We focus on the value of a (such as resources development) project in general depends on the price of the multiple products; these are usually correlated to some extent. So the project was treated as having a rainbow option, whose underlying asset prices correlate with each other, and also as having uncertainties that decrease according to the project stage. Based on Cherubini and Luciano’s framework (2002), the risk-neutral copula models are derived to figure decision flexibilities out easily. The main framework studies the valuation of a project (call on Max) by determining the joint risk-neutral distribution of the underlying assets (products) using copulas. Monte-Carlo simulations show that the higher default risk and association among the assets and the expected cost to completion contributes the higher risk premium in our model with dependence structure of Archimedean copula family than traditional Black-Scholes environment.

The goal of this project is to price multi-name credit derivatives using a copula approach. The properties and advantage copula functions have to other traditional methods are carefully evaluated. Monte Carlo simulations are studied and performed to obtain numerical results for copula functions with explicit and implicit forms. A model was developed to price a basic form of a first-to-default basket using different copula functions. The outcomes are analyzed and comparisons are carried out.

O interesse pelos estudos de bioequivalência iniciou-se na década de 60, sendo o FDA (EUA) a primeira agência reguladora a se interessar por esta questão. No Brasil, uma lei de 1999 regulamentou o medicamento genérico no país, sendo este um importante meio de acesso aos medicamentos pela população e fazendo parte da política de medicamentos do SUS. No Brasil, a ANVISA e responsável por inspecionar os centros de bioequivalência bem como dar as diretrizes para estes. Um modelo paramétrico padrão para a etapa estatística e disponibilizado para a decisão de bioequivalência media e espera-se que este ajuste-se aos dados obtidos nos estudos de bioequivalência, o que nem sempre acontece. Neste sentido, e proposto nesta tese o uso de modelos paramétricos mais abrangentes baseados em outras distribuições de probabilidade para a decisão de bioequivalência media e que possam modelar a assimetria dos dados, dispensando o uso da transformação logarítmica para os parâmetros farmacocinéticos o que afeta a amplitude dos limites de bioequivalência. Propõe-se também o uso de modelos bivariados para a tomada conjunta da decisão de bioequivalência media, quando são analisados simultaneamente dois parâmetros farmacocinéticos. Foram utilizados métodos Bayesianos para a estimação dos parâmetros dado a exibilidade deste enfoque quando combinado ao uso dos métodos MCMC facilitados a partir do uso de softwares livres. Nesta tese e apresentado um estudo do poder empírico dos testes de hipóteses para os modelos univariados propostos bem como são introduzidos quatro exemplos, sendo os três primeiros voltados a aplicação da decisão de bioequivalência media e o quarto para a aplicação da bioequivalência populacional e individual. Nos três primeiros exemplos foram observados ganhos em termos de ajuste dos novos modelos propostos aos dados com relação ao modelo padrão segundo os critérios de seleção de modelos utilizados. O exemplo quatro apresenta uma analise padrão de bioequivalência populacional e individual com o código computacional para a obtenção dos resultados disponível no apêndice A bem como outros códigos para os demais exemplos. Embora a padroniza- ção das análises estatísticas para os estudos de bioequivalência seja importante, não deve-se esperar que um modelo padrão ajuste-se a qualquer conjunto de dados originados destes tipo de estudos. Neste sentido, são apresentados alternativas que podem auxiliar o pesquisador na tomada de uma decisão em termos de bioequivalência media mais segura. / The interest in bioequivalence studies began in the early 1960s especially in the United States of America where the FDA was the rst regulatory agency to show interest upon this issue. In Brazil, this interest started in 1999 the year when a law regulated the generic drugs in the country. The ANVISA is the Brazilian regulatory agency responsible for inspecting the bioequivalence centers and giving guidelines for this issue. In general, a standard parametric model for the statistical step is indicated for the average bioequivalence decision and this model is expected to be tted by the data obtained in the bioequivalence studies. In some cases, this model would not be appropriate. In this way, this thesis proposes the use of more comprehensive parametric models based on other probability distributions for the average bioequivalence decision and that can model asymmetrical data, a common situation in bioequivalence studies. In addition, there is no need of a logarithmic transformation for the pharmacokinetic parameters which could aect the range of the bioequivalence limits. We also propose the use of parametrical bivariate models for the joint decision of the average bioequivalence decision, since these measures are usually analyzed simultaneously with two pharmacokinetic parameters. We use Bayesian methods to estimate the parameters, given the great exibility of this approach when combined with the use of MCMC methods using free available softwares. This thesis also presents a study of the empirical power of hypothesis testing for the proposed univariate models and four examples are introduced. In the examples one, two and three we apply the average bioequivalence decision and in the fourth example we consider for the implementation of population and individual bioequivalence. In the examples one, two and three were observed gains in the tting of the proposed new models for the data where some existing approaches were used in the selection criteria for the proposed models. Example four provides a standard analysis of population and individual bioequivalence with the computer code for obtaining the results available in the Appendix A, as well as other codes. Although the standardization of statistical analysis for bioequivalence studies is important, a standard model is not expected to be well tted to any data set originated by such studies. In this way, we present alternatives that can help researchers in making a decision in terms of average bioequivalence with more security.

O interesse pelos estudos de bioequivalência iniciou-se na década de 60, sendo o FDA (EUA) a primeira agência reguladora a se interessar por esta questão. No Brasil, uma lei de 1999 regulamentou o medicamento genérico no país, sendo este um importante meio de acesso aos medicamentos pela população e fazendo parte da política de medicamentos do SUS. No Brasil, a ANVISA e responsável por inspecionar os centros de bioequivalência bem como dar as diretrizes para estes. Um modelo paramétrico padrão para a etapa estatística e disponibilizado para a decisão de bioequivalência media e espera-se que este ajuste-se aos dados obtidos nos estudos de bioequivalência, o que nem sempre acontece. Neste sentido, e proposto nesta tese o uso de modelos paramétricos mais abrangentes baseados em outras distribuições de probabilidade para a decisão de bioequivalência media e que possam modelar a assimetria dos dados, dispensando o uso da transformação logarítmica para os parâmetros farmacocinéticos o que afeta a amplitude dos limites de bioequivalência. Propõe-se também o uso de modelos bivariados para a tomada conjunta da decisão de bioequivalência media, quando são analisados simultaneamente dois parâmetros farmacocinéticos. Foram utilizados métodos Bayesianos para a estimação dos parâmetros dado a exibilidade deste enfoque quando combinado ao uso dos métodos MCMC facilitados a partir do uso de softwares livres. Nesta tese e apresentado um estudo do poder empírico dos testes de hipóteses para os modelos univariados propostos bem como são introduzidos quatro exemplos, sendo os três primeiros voltados a aplicação da decisão de bioequivalência media e o quarto para a aplicação da bioequivalência populacional e individual. Nos três primeiros exemplos foram observados ganhos em termos de ajuste dos novos modelos propostos aos dados com relação ao modelo padrão segundo os critérios de seleção de modelos utilizados. O exemplo quatro apresenta uma analise padrão de bioequivalência populacional e individual com o código computacional para a obtenção dos resultados disponível no apêndice A bem como outros códigos para os demais exemplos. Embora a padroniza- ção das análises estatísticas para os estudos de bioequivalência seja importante, não deve-se esperar que um modelo padrão ajuste-se a qualquer conjunto de dados originados destes tipo de estudos. Neste sentido, são apresentados alternativas que podem auxiliar o pesquisador na tomada de uma decisão em termos de bioequivalência media mais segura. / The interest in bioequivalence studies began in the early 1960s especially in the United States of America where the FDA was the rst regulatory agency to show interest upon this issue. In Brazil, this interest started in 1999 the year when a law regulated the generic drugs in the country. The ANVISA is the Brazilian regulatory agency responsible for inspecting the bioequivalence centers and giving guidelines for this issue. In general, a standard parametric model for the statistical step is indicated for the average bioequivalence decision and this model is expected to be tted by the data obtained in the bioequivalence studies. In some cases, this model would not be appropriate. In this way, this thesis proposes the use of more comprehensive parametric models based on other probability distributions for the average bioequivalence decision and that can model asymmetrical data, a common situation in bioequivalence studies. In addition, there is no need of a logarithmic transformation for the pharmacokinetic parameters which could aect the range of the bioequivalence limits. We also propose the use of parametrical bivariate models for the joint decision of the average bioequivalence decision, since these measures are usually analyzed simultaneously with two pharmacokinetic parameters. We use Bayesian methods to estimate the parameters, given the great exibility of this approach when combined with the use of MCMC methods using free available softwares. This thesis also presents a study of the empirical power of hypothesis testing for the proposed univariate models and four examples are introduced. In the examples one, two and three we apply the average bioequivalence decision and in the fourth example we consider for the implementation of population and individual bioequivalence. In the examples one, two and three were observed gains in the tting of the proposed new models for the data where some existing approaches were used in the selection criteria for the proposed models. Example four provides a standard analysis of population and individual bioequivalence with the computer code for obtaining the results available in the Appendix A, as well as other codes. Although the standardization of statistical analysis for bioequivalence studies is important, a standard model is not expected to be well tted to any data set originated by such studies. In this way, we present alternatives that can help researchers in making a decision in terms of average bioequivalence with more security.

Os modelos de fragilidade são utilizados para modelar as possíveis associações entre os tempos de sobrevivência. Uma outra alternativa desenvolvida para modelar a dependência entre dados multivariados é o uso dos modelos baseados em funções cópulas. Neste trabalho propusemos dois modelos de sobrevivência derivados das cópulas de Ali- Mikhail-Haq (AMH) e de Frank para modelar a dependência de dados bivariados na presença de covariáveis e observações censuradas. Para fins inferenciais, realizamos uma abordagem bayesiana usando métodos Monte Carlo em Cadeias de Markov (MCMC). Algumas discussões sobre os critérios de seleção de modelos são apresentadas. Com o objetivo de detectar observações influentes utilizamos o método bayesiano de análise de influência de deleção de casos baseado na divergência ψ. Por fim, mostramos a aplicabilidade dos modelos propostos a conjuntos de dados simulados e reais. Apresentamos, também, um novo modelo de sobrevivência bivariado com fração de cura, que leva em consideração três configurações para o mecanismo de ativação latente: ativação aleatória, primeira ativação é última ativação. Aplicamos este modelo a um conjunto de dados de empréstimo de Crédito Direto ao modo do Consumidor (DCC) e comparamos os ajustes por meio dos critérios bayesianos de seleção de modelos para verificar qual dos três modelos melhor se ajustou. Por fim, mostramos nossa proposta futura para a continuação da pesquisa. / The frailty models are used to model the possible associations between survival times. Another alternative developed for modeling the dependence between multivariate data is the use of models based on copulas functions. In this paper we propose two derived survival models of copula of the Ali-Mikhail-Haq (AMH) and of the Frank to model the dependence of bivariate data in the presence of covariates and censored observations. For inferential purposes, we conducted a Bayesian approach using Monte Carlo methods in Markov Chain (MCMC). Some discussions on the model selection criteria were presented. In order to detect influential observations we use the Bayesian method of cases of deletion of influence analysis based on the difference ψ. Finally, we show the applicability of the proposed models to sets of simulated and real data. We present, too, a new survival model with bivariate fraction of healing, which takes into account three settings for the latent activation mechanism: random activation, first activation and final activation. We apply this model to a set of Direct Credit loan data to the Consumer mode (DCC) and compare the settings, through Bayesian criteria for selection of models, which of the three models best fit. Finally, we show our future proposal for further research.

Os modelos de fragilidade são utilizados para modelar as possíveis associações entre os tempos de sobrevivência. Uma outra alternativa desenvolvida para modelar a dependência entre dados multivariados é o uso dos modelos baseados em funções cópulas. Neste trabalho propusemos dois modelos de sobrevivência derivados das cópulas de Ali- Mikhail-Haq (AMH) e de Frank para modelar a dependência de dados bivariados na presença de covariáveis e observações censuradas. Para fins inferenciais, realizamos uma abordagem bayesiana usando métodos Monte Carlo em Cadeias de Markov (MCMC). Algumas discussões sobre os critérios de seleção de modelos são apresentadas. Com o objetivo de detectar observações influentes utilizamos o método bayesiano de análise de influência de deleção de casos baseado na divergência ψ. Por fim, mostramos a aplicabilidade dos modelos propostos a conjuntos de dados simulados e reais. Apresentamos, também, um novo modelo de sobrevivência bivariado com fração de cura, que leva em consideração três configurações para o mecanismo de ativação latente: ativação aleatória, primeira ativação é última ativação. Aplicamos este modelo a um conjunto de dados de empréstimo de Crédito Direto ao modo do Consumidor (DCC) e comparamos os ajustes por meio dos critérios bayesianos de seleção de modelos para verificar qual dos três modelos melhor se ajustou. Por fim, mostramos nossa proposta futura para a continuação da pesquisa. / The frailty models are used to model the possible associations between survival times. Another alternative developed for modeling the dependence between multivariate data is the use of models based on copulas functions. In this paper we propose two derived survival models of copula of the Ali-Mikhail-Haq (AMH) and of the Frank to model the dependence of bivariate data in the presence of covariates and censored observations. For inferential purposes, we conducted a Bayesian approach using Monte Carlo methods in Markov Chain (MCMC). Some discussions on the model selection criteria were presented. In order to detect influential observations we use the Bayesian method of cases of deletion of influence analysis based on the difference ψ. Finally, we show the applicability of the proposed models to sets of simulated and real data. We present, too, a new survival model with bivariate fraction of healing, which takes into account three settings for the latent activation mechanism: random activation, first activation and final activation. We apply this model to a set of Direct Credit loan data to the Consumer mode (DCC) and compare the settings, through Bayesian criteria for selection of models, which of the three models best fit. Finally, we show our future proposal for further research.

Orientador: Jorge Alberto Achcar / Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Matemática, Estatística e Computação Científica / Made available in DSpace on 2018-08-18T02:57:38Z (GMT). No. of bitstreams: 1 TovarCuevas_JoseRafael_D.pdf: 2314079 bytes, checksum: 3de8e433bd4d02c785316e5d57f1a980 (MD5) Previous issue date: 2011 / Resumo: A maioria dos estudos sobre estimação da prevalência e parâmetros de desempenho de testes para diagnóstico clínico não tem considerado que muitos dos métodos de diagnóstico incluem a medição de traços biológicos cuja resposta é expressa em escala contínua e que, devido ao fato de serem medidos no mesmo indivíduo, esses traços necessariamente apresentam algum tipo de dependência que pode ou não ser explicada como um fenômeno de comportamento linear ou de concordância. Além disso, a análise de dados realizada nesses estudos parte do pressuposto de que a estrutura dos testes é binária sem considerar o fato de que as observações assumem essa apresentação depois de serem dicotomizadas usando um ponto de corte estabelecido a partir de critérios clínicos. Nesta tese, apresenta-se uma proposta de abordagem Bayesiana ao problema da estimação da prevalência, da sensibilidade e da especificidade dos testes dentro de planejamentos que incluem a aplicação de dois ou três testes diagnósticos de triagem, os quais são produto da medição de igual número de traços biológicos expressos em escala contínua com ponto de corte para dicotimização e um padrão-ouro para verificação. Embora o objetivo principal do modelo estatístico proposto seja estudar o efeito da dependência entre resultados dos testes de triagem sobre as estimativas da prevalência e os parâmetros de desempenho, também se consideram alternativas para contornar outras dificuldades comuns neste tipo de estudos, como a falta de identificabilidade e o viés devido à não verificação com padrão-ouro de indivíduos com resultado negativo em ambos os testes de triagem (viés de verificação). A proposta considera o uso de três funções cópula para modelar a dependência e a avaliação de três níveis da mesma. Dado o enfoque Bayesiano do estudo, foi necessário desenvolver um procedimento para elicitar distribuições a priori em situações de total ausência de informação sobre o parâmetro de interesse, o que acontece com as cópulas, funções bastante desconhecidas na pesquisa médica. Os resultados obtidos com o modelo proposto foram comparados com aqueles obtidos utilizando a covariância como parâmetro de dependência e o pressuposto de independência. O modelo apresenta uma reparametrização que, a diferença da maioria dos métodos apresentados na literatura sobre o tema, permite obter diretamente as estimativas de interesse sem a necessidade de complexos procedimentos analíticos e computacionais. A presença de dependência tem pouco efeito sobre a estimativa da prevalência e afeta as estimativas dos parâmetros de desempenho, o efeito é mais forte quando o planejamento apresenta viés de verificação. Dependências fracas subestimam as sensibilidades e os outros parâmetros não apresentam viés, enquanto que dependências fortes superestimam todos os parâmetros. Nos casos em que os traços biológicos medidos não apresentam fortes modificações devido à presença da enfermidade (ou infecção) no indivíduo, as estimativas podem chegar a tomar valores 50% maiores que o valor real, o que pode implicar importantes erros na tomada de decisões relacionadas à forma de tratar a doença / Abstract: Most studies to estimate the prevalence and performance clinical diagnostic test parameters have not considered that many of the diagnostic methods include the measurement of biological traits with outcome expressed in a continuous scale and that, due to these traits, are measured on the same individual, they necessarily have some kind of dependence that may or not be explained as a phenomenon of linear relation or agreement. Generally authors assume that the data have binary structure and they do not consider the fact the data take that form after of they be dichotomized using a cut-off. In this thesis, it is developed a proposal based on a Bayesian approach to the problem of estimating the prevalence, the sensitivity and the specificity of tests within designs that include the application of a gold standard for verification and two or three screening diagnostic tests each of them resulting from a measurement of a biological trait expressed in a continuous scale and dichotomization. Although the main objective of the proposed statistical model is to study the effect of dependence between test results on prevalence and performance test parameter estimates, it is also studied some alternatives found in the literature to address common difficulties in diagnostic test studies such as the lack of identifiability and the verification bias (specially when individuals with negative results in both screening tests are not verified by "gold standard"procedure). The proposed estimation method considers the use of three copula functions to study the effect of same number of dependence levels on the parameter test estimates. Since the study is based on a Bayesian approach, it was necessary to develop a procedure to eliciting prior distributions in situations of total absence of information about the parameter of interest, as is the case of copula functions that have been very little used in medical research. The obtained results are compared with those obtained using binary covariance and independence between test outcomes assumption, methods frequently used by other authors. Unlike the majority of methods presented in the literature on the matter, the proposed estimation model has a reparametrization that gives the estimates of interest directly without need of use complex analytical and computational methods and the results are easily obtained using a Winbugs 1.4. program. The dependence affects the estimates of the test parameters and it has little effect on the prevalence estimate. The effect is stronger in presence of verification bias. Weak dependences underestimate the sensitivities and other parameters are unbiased, while strong dependencies overestimate all parameters. In situations in which the biological traits measured did not show strong changes due to the presence of the disease (or infection) on the individual, the estimates can reach values close to 50% higher than the real value, which may involve important errors in decision making related to how to treat the disease / Doutorado / Estatistica e Probabilidade / Doutor em Estatística

Initialement, la modélisation des risques en assurance non vie, supposait l'indépendance entre les différentes variables des modèles actuariels. De nos jours, cette hypothèse d'indépendance est souvent relâchée afin de tenir compte de possibles interactions entre les différents éléments. Cette thèse a pour but de contribuer à la littérature existante de la modélisation de la dépendance en assurance non vie. Concrètement, nous introduisons une nouvelle méthodologie d'analyse des risques en assurance à travers le développement des modèles de dépendance, principalement dans un cadre dynamique. Dans le premier chapitre de la thèse nous introduisons le contexte actuel de solvabilité, ainsi que la modélisation de la dépendance en assurance, avec une présentation des principaux résultats. Le deuxième chapitre est essentiellement constitué d'un article coécrit avec Christian de Peretti et Lotfi Belkacem, intitulé "Modelling Temporal Dependence of Claims In Insurance Using Autoregressive Conditional Amount Models" (voir Araichi et al. (2013)). Dans ce chapitre nous montrons l'existence d'une forme de dépendance temporelle (dynamique) entre les montants de sinistres d'une même branche d'assurance. Nous proposons un nouveau modèle nommé Autoregressive Conditional Amount Model (ACA), qui permet de capturer le comportement dynamique des sinistres. Également, nous développons un nouveau modèle nommé Generalized Extreme Value ACA model (GEVACA), afin d'analyser la dépendance dynamique des montants élevés, au niveau des queues de distribution. Enfin, nous donnons une nouvelle expression pour la Value at Risk (VaR) paramétrique adaptée pour des risques à dépendance temporelle. Des applications sur des données réelles et des techniques de backtesting sont ensuite effectuées afin de montrer la pertinence des modèles proposés. Le troisième chapitre est constitué d'un article coécrit avec Christian de Peretti et Lotfi Belkacem, intitulé "Generalized Autoregressive Conditional Sinistrality Model : A novel model for claims reserving in Non life insurance", (voir Araichi et al. (2015)). Dans ce chapitre, nous abordons d'abord le problème de l'évaluation des réserves dans un cadre dynamique. Nous montrons l'existence d'une forme de dépendance dynamique dans un triangle de liquidation. En particulier, nous nous intéressons à l'analyse de la dépendance temporelle entre les sinistres, ainsi qu'entre les années de développement. Nous proposons un nouveau modèle nommé "Generalized Autoregressive Conditional Sinistrality Model (GACSM), qui constitue une extension du modèle linéaire généralisé classique. Ensuite, nous fournissons une méthode de simulation bootstrap basée sur le modèle GACSM, qui permet d'évaluer les réserves en tenant compte du caractère dynamique des sinistres. Enfin, afin de montrer l'impact du modèle proposé sur l'évaluation des réserves et du capital, nous effectuons une comparaison des résultats obtenus avec ceux obtenus des modèles classiques (Chain Ladder et modèle linéaire généralisé). Dans le quatrième chapitre de la thèse, qui est constitué d'un article, coécrit avec Christian de Peretti et Lotfi Belkacem, intitulé "Time Varying Copula Model for claims reserving in Non life insurance". Nous intéressons à évaluer le montant agrégé des sinistres, en analysant conjointement la dépendance dynamique inter-sinistres ainsi qu'entre les sinistres de deux branches. Nous proposons un modèle basé sur le modèle GACSM et les copules conditionnelles, qui permettent de suivre l'évolution de la dépendance au cours du temps. Enfin, nous effectuons des applications sur des données réelles, ainsi que des méthodes de simulation sont considérées. En comparant les résultats obtenus, nous avons pu illustrer l'impact de la dépendance dynamique sur les réserves et le besoin en capital / In this thesis a different aspects of dependence modeling are considered. Indeed, temporal dependence structures between claims amounts and between lines of business are analyzed. In the first chapter, a general introduction on modeling dependence in insurance is provided. The second chapter is essentially constituted by the article "Modeling Temporal Dependence of Claims In Insurance Using Autoregressive Conditional Amount Models", written with Christian de Peretti and Lotfi Belkacem, (see Araichi et al. (2013)) It deals with the problem of existing a temporal dependence structure between claims amounts of one line of business. To this end, we propose a new model for handling the dynamic behaviour of claims amounts in insurance companies using an Autoregressive Conditional Amount (ACA) framework. This model will be named Autoregressive Conditional Amount Model (ACA). A Gamma ACA model and a Generalized Extreme Value ACA model are proposed. It is shown that these models are more appropriate to describe and to forecast the process of claims of the lines Auto Damage and Auto Liability than traditional models. Furthermore, a parametric Value at Risk based on ACA framework (VaR ACA) is proposed for evaluating a coverage amount of these claims. Using backtesting techniques, the VaR ACA provides an accurate estimation of risk. The third chapter of this thesis is based on the article "Generalized Autoregressive Conditional Sinistrality Model: A novel model for claims reserving in Non life insurance", written with Christian de Peretti and Lotfi Belkacem, (see Araichi et al. (2015)). In this chapter, a Generalized Autoregressive Conditional Sinistrality Model (GACSM) for claims is proposed. We extend the Generalized Linear Model (GLM) by incorporating temporal dependence between claims amounts of one triangle. The GACSM is used for model parameter estimation and consistency of such estimate is proved. Bootstrap procedure is implemented for prediction reserves and prediction errors. Results show that taking into account the temporal dependence between losses improves the precision of the reserve distribution estimate, and thus evaluates an accurate SCR. Finally the fourth chapter is based on the article "Time Varying Copula Model for claims reserving in Non life insurance", written with Christian de Peretti and LotfiBelkacem. In this chapter, a time varying copula models to understand the behavior of claims amounts of two lines of business. Time varying copula functions with a Generalized Autoregressive Conditional Sinistrality model are used to analyze the evolution in time of dependence between two lines and the temporal dependence between claims of each line. Simulation study is performed to highlight the impact on reserves and Solvency Capital Requirement. Results show that our approach provides a diversification effect between claims amounts

A técnica de análise de sobrevivência tem sido muito utilizada por pesquisadores na área de saúde. Neste trabalho foi usada uma distribuição em análise de sobrevivência recentemente estudada, chamada distribuição exponencial generalizada. Esta distribuição foi estudada sob todos os aspectos: para dados completos e censurados, sob a presençaa de covariáveis e considerando sua extensão para um modelo multivariado derivado de uma função cópula. Para exemplificação desta nova distribuição, foram utilizados dados reais de câncer (leucemia mielóide aguda e câncer gástrico) que possuem a presença de censuras e covariáveis. Os dados referentes ao câncer gástrico tem a particularidade de apresentar dois tempos de sobrevida, um relativo ao tempo global de sobrevida e o outro relativo ao tempo de sobrevida livre do evento, que foi utilizado para a aplicação do modelo multivariado. Foi realizada uma comparação com outras distribuições já utilizadas em análise de sobrevivência, como a distribuiçãoo Weibull e a Gama. Para a análise bayesiana adotamos diferentes distribuições a priori para os parâmetros. Foi utilizado, nas aplicações, métodos de simulação de MCMC (Monte Carlo em Cadeias de Markov) e o software Winbugs. / Survival analysis methods has been extensively used by health researchers. In this work it was proposed the use a survival analysis model recently studied, denoted as generalized exponential distribution. This distribution was studied in all respects: for complete data and censored, in the presence of covariates and considering its extension to a multivariate model derived from a copula function. To exemplify the use of these models, it was considered real cancer lifetime data (acute myeloid leukemia and gastric cancer) in presence of censored data and covariates. The assumed cancer gastric lifetime data has two survival responses, one related to the total lifetime of the patient and another one related to the time free of the disease, that is, multivariate data associated to each patient. In these applications there was considered a comparative study with standard existing lifetime distributions, as Weibull and gamma distributions.For a Bayesian analysis we assumed different prior distributions for the parameters of the model. For the simulation of samples of the joint posterior distribution of interest, we used standard MCMC (Markov Chain Monte Carlo) methods and the software Winbugs.