The determination of the sufficient amount of economic capital and its allocation to the business lines is the key issue for insurance companies. In this thesis we introduce two methods of aggregating economic capital. One is based on linear correlation and the second deals with copulas. A multitude of allocation principles have been proposed in the literature. We choose those which are the most used in practice and compare advantages and disadvantages of their application. The last chapter is devoted to the numerical examples of capital aggregation and allocation principles. 1

Thesis advisor: Laura M. O'Dwyer / Education researchers are frequently interested in examining the causal impact of academic services and interventions; however, it is often not feasible to randomly assign study elements to treatment conditions in the field of education (Adelson, 2013). When assignment to treatment conditions is non-random, the omission of any variables relevant to treatment selection creates a correlation between the treatment variable and the error in regression models. This is termed endogeneity (Ebbes, 2004). In the presence of endogeneity, treatment effect estimates from traditionally used regression approaches may be biased. The purpose of this study was to investigate the causal impact of an integrated student support model, namely City Connects, on student academic achievement. Given that students are not randomly assigned to the City Connects intervention, endogeneity bias may be present. To address this issue, two novel and underused statistical approaches were used with school admissions lottery data, namely Gaussian copula regression developed by Park and Gupta (2012), and Latent Instrumental Variable (LIV) regression developed by Peter Ebbes (2004). The use of real-world school admissions lottery data allowed the first-ever comparison of the two proposed methods with Instrumental Variable (IV) regression under a large-scale randomized control (RCT) trial. Additionally, the researcher used simulation data to investigate both the performance and boundaries of the two proposed methods compared with that of OLS and IV regression. Simulation study findings suggest that both Gaussian copula and LIV regression are useful approaches for addressing endogeneity bias across a range of research conditions. Furthermore, simulation findings suggest that the two proposed methods have important differences in their set of identifying assumptions, and that some assumptions are more crucial than others. Results from the application of the Gaussian copula and LIV regression in the City Connects school lottery admissions study demonstrated that receiving the City Connects model of integrated student support during elementary school has a positive impact on mathematics achievement. Such findings underscore the importance of addressing out-of-school barriers to learning. / Thesis (PhD) — Boston College, 2019. / Submitted to: Boston College. Lynch School of Education. / Discipline: Educational Research, Measurement and Evaluation.

A thesis submitted to the Faculty of Science, University of the Witwatersrand, Johannesburg, in fulfilment of the requirements for the degree of Doctor of Philosophy. Johannesburg, December 2014. / Industrial units cannot operate without failure forever. When the operation of a unit deviates from industrial standards, it is considered to have failed. The time from the moment a unit enters service until it fails is its lifetime. Within reliability and often in life data analysis in general, lifetime is the event of interest. For highly reliable units, accelerated life testing is required to obtain lifetime data quickly. Accelerated tests where failure is not instantaneous, but the end point of an underlying degradation process are considered. Failure during testing occurs when the performance of the unit falls to some specified threshold value such that the unit fails to meet industrial specifications though it has some residual functionality (degraded failure) or decreases to a critical failure level so that the unit cannot perform its function to any degree (critical failure). This problem formulation satisfies the random signs property, a notable competing risks formulation originally developed in maintenance studies but extended to accelerated testing here. Since degraded and critical failures are linked through the degradation process, the open problem of modelling dependent competing risks is discussed. A copula model is assumed and expert opinion is used to estimate the copula. Observed occurrences of degraded and critical failure times are interpreted as times when the degradation process first crosses failure thresholds and are therefore postulated to be distributed as inverse Gaussian. Based on the estimated copula, a use-level unit lifetime distribution is extrapolated from test data. Reliability metrics from the extrapolated use-level unit lifetime distribution are found to differ slightly with respect to different degrees of stochastic dependence between the risks. Consequently, a degree of dependence between the risks that is believed to be realistic to admit is considered an important factor when estimating the use-level unit lifetime distribution from test data. Keywords: Lifetime; Accelerated testing; Competing risks; Copula; First passage time.

Motivados por um conjunto de dados de pacientes com insuficiência renal crônica (IRC), propomos uma nova modelagem bayesiana que envolve cópulas da família Arquimediana e um modelo misto para dados de sobrevivência com riscos semicompetitivos. A estrutura de riscos semicompetitivos é bastante comum em estudos clínicos em que dois eventos são de interesse, um intermediário e outro terminal, de forma tal que a ocorrência do evento terminal impede a ocorrência do intermediário mas não vice-versa. Nesta modelagem provamos que a distribuição a posteriori sob a cópula de Clayton é própria. Implementamos os algoritmos de dados aumentados e amostrador de Gibbs para a inferência bayesiana, assim como os criterios de comparação de modelos: LPML, DIC e BIC. Realizamos um estudo de simulação para avaliar o desempenho da modelagem e finalmente aplicamos a metodologia proposta para analisar os dados dos pacientes com IRC, além de outros de pacientes que receberam transplante de medula óssea. / Motivated by a dataset of patients with chronic kidney disease (CKD), we propose a new bayesian model including the Arquimedean copula and a mixed model for survival data with semicompeting risks. The structure of semicompeting risks appears frequently in clinical studies where two-types of events are involved: a nonterminal and a terminal event such that the occurrence of terminal event precludes the occurrence of the non-terminal event but not viceversa. In this work we prove that the posterior distribution is proper when the Clayton copula is used. We implement the data augmentation algorithm and Gibbs sampling for the bayesian inference, as well as some bayesian model selection criteria: LPML, BIC and DIC. We carry out a simulation study for assess the model performance and finally, our methodology is illustrated with the chronic kidney disease study.

Neste trabalho objetivou-se estudar o comportamento de acasalamento de Cyrtomon luridus Boheman (Coleoptera: Curculionidae), bem como a presença de semioquímicos mediando o acasalamento e a interação com a planta hospedeira Duboisia sp. (Solanaceae). Machos e fêmeas adultos recém-emergidos foram coletados no campo e levados para o laboratório. Incialmente foi determinado o melhor parâmetro morfológico para diferenciação de machos e fêmeas. Verificou-se que machos deste curculionídeo possuem a abertura genital oclusa pelo último tergito. O comportamento de acasalamento foi observado em casais virgens durante nove dias. Verificou-se que machos e fêmeas de C. luridus atingiram a maturidade sexual dois dias após a emergência. Machos e fêmeas realizaram acasalamentos repetidos com o mesmo parceiro em qualquer horário do dia. O comportamento de acasalamento deste curculionídeo foi dividido nas fases pré-copulatória, copulatória e pós-copulatória. Além disso, estudos de olfatometria revelaram que machos e fêmeas de C. luridus foram fortemente atraídos por voláteis de machos se alimentando sobre a planta hospedeira. A coleta e análise destes voláteis revelaram a presença dos compostos (Z)-3-hexenal, hexanal, (E)-2-hexenal, (E)-2-hexen-1-ol, fenilacetaldeido, linalol e geraniol, como eletrofisiologicamente ativos. O presente trabalho traz importantes informações sobre o comportamento de acasalamento e ecologia química de Entiminae e servirão de base para estudos com outras espécies desta importante subfamília de Curculionidae. / This work aimed to study the mating behavior of Cyrtomon luridus Boheman (Coleoptera: Curculionidae), as well as the presence of semiochemicals mediating the mating and the interaction of the insects with the host plant, Duboisia sp. (Solanaceae). Newly emerged males and females adults were collected in the field and taken to the laboratory. Initially it determined the best morphological parameter to differentiate males and females. It was found that males possess the genital opening occluded by the last tergite. The mating behavior was observed in virgin couples for nine days. It was found that males and females C. luridus reached sexual maturity two days after emergence. Males and females made repeated matings with the same partner at any time of day. The mating behavior was clearly divided into the pre-copulatory, copulatory, and post-copulatory phases. In addition, olfatometrics studies revealed that males and females C. luridus were strongly attracted to volatile males feeding on the host plant. The collection and analysis of these volatiles revealed the compounds (Z)-3-hexenal, hexanal, (E)-2-hexenal, (E)-2-hexen-1-ol, phenylacetaldehyde, linalool and geraniol as being eletrophysiologically. The present work brings important information about the mating behavior and chemical ecology of Entiminae, which will serve as support for studies with other species of this important subfamily of Curculionidae.

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.

No presente trabalho, exploramos dois temas de interesse em finanças, economia e antropologia social, através da aplicação de técnicas da teoria da informação e da mecânica estatística. No primeiro tópico, estudamos a conexão entre teoria de dependência estatística, teoria de informação e teoria da cópulas. O conceito de distribuição cópula é revisto e aplicado em reformulação das definições de medida de dependência dadas por Rényi 1. Em seguida, mostramos que a informação mútua satisfaz todos os requisitos para ser uma boa medida de dependência. Obtemos uma identidade entre a informação mútua e a entropia da distribuição cópula e uma decomposição mais específica da informação mútua de uma distribuição elíptica nas suas partes linear e não-linear. Avaliamos o risco de usar quantidades ingênuas como medidas de dependência estatística, mostrando que a correlação linear pode subestimar grosseiramente a dependência. Esses resultados são utilizados para desenvolver um método de detectação de desvios de dependência gaussiana em pares de variáveis aleatórias e aplicá-lo a séries temporais financeiras. Finalmente, discutimos um método para ajustar t-cópulas a dados empíricos 2 através da medida da informação mútua e do tau de Kendall. No segundo tópico, desenvolvemos um modelo para o surgimento de autoridade em sociedades humanas pré-agrícolas. Discutimos motivações empíricas com raízes em neurociência, primatologia e antropologia para um modelo matemático capaz de explicar a ampla variabilidade de formas de organização social humana no eixo igualitário hierárquico. O modelo resulta da aplicação de teoria da informação a uma hipótese sobre os custos evolutivos envolvidos na vida social. O modelo gera um diagrama de fase rico, com diferentes regimes que podem ser interpretados como diferentes tipos de organização social. Os parâmetros de controler do modelo estão ligados à capacidade cognitiva da espécie em questão, ao tamanho do grupo e a pressões ecológicas e sociais. / In the present work we explore two topics of interest in finance, economics and social anthropology through the application of techniques from information theory and statistical mechanics. In the first topic we study the connexion between statistical dependency theory, information theory and copula theory. The concept of copula distribution is reviewed and applied to the reformulation of the definition of dependency measures given by Rényi 3. It is then shown that the mutual information satisfy all the requirements to be a good dependency measure. We derive an identity between mutual information and the entropy of the copula distribution and a more specific decomposition of the mutual information of an elliptical distribution into its linear and non-linear parts. We evaluate the risk of using naive measures as statistical dependency measures by showing that linear correlation can grossly underestimate dependency. Those results are used to develop a method to detect deviation from gaussian dependence in pairs of random variables and apply it to financial time series. Finally, we discuss a method to adjust t-copulas to empirical data4 through the determination of the mutual information and Kendalls tau. In the second topic we develop a model for the emergence of authority in pre-agricultural human societies. We discuss empirical motivations with roots in neuroscience, primatology and anthropology for a mathematical model able to explain the ample variability of forms of human social organization in the egalitarian-hierarchical axis. The model results from the application of information theory on a hypothesis about the evolutive costs involved in social life. It generates a rich phase diagram, with different regimes which can be interpreted as different types of societal organization, from egalitarian to hierarchical. The control parameters of the model are connected to the cognitive capacity of the species in question, the size of the group and ecological and social pressures.

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.

Asset and Liability Management (ALM) models have become well established decision tools for pension funds. ALMs are commonly modelled as multi-stage, in which a large terminal wealth is required, while at intermediate time periods, constraints on the funding ratio, that is, the ratio of assets to liabilities, are imposed. Underfunding occurs when the funding ratio is too low; a target value for funding ratios is pre-specified by the decision maker. The risk of underfunding has been usually modelled by employing established risk measures; this controls one single aspect of the funding ratio distributions. For example, controlling the expected shortfall below the target has limited power in controlling shortfall under worst-case scenarios. We propose ALM models in which the risk of underfunding is modelled based on the concept of Second Order Stochastic Dominance (SSD). This is a criterion of ranking random variables - in our case funding ratios - that takes the entire distributions of interest into account and works under the widely accepted assumptions of decision makers being rational and risk averse. In the proposed SSD models, investment decisions are taken such that the resulting short-term distribution of the funding ratio is non-dominated with respect to SSD, while a constraint is imposed on the expected terminal wealth. This is done by considering progressively larger tails of the funding ratio distribution and considering target levels for them; a target distribution is thus implied. Different target distributions lead to different SSD efficient solutions. Improved distributions of funding ratios may be thus achieved, compared to the existing risk models for ALM. This is the first contribution of this thesis. Interesting results are obtained in the special case when the target distribution is deterministic, specified by one single outcome. In this case, we can obtain equivalent risk minimisation models, with risk defined as expected shortfall or as worst case loss. This represents the second contribution. The third contribution is a framework for scenario generation based on the "Birth, Immigration, Death, Emigration" (BIDE) population model and the Empirical copula; the scenarios are used to evaluate the proposed models and their special cases both in-sample and out-of-sample. As an application, we consider the planning problem of a large DB pension fund in Saudi Arabia.