In this dissertation, we develop several new inference procedures that are based on randomized nomination sampling (RNS). The first problem we consider is that of constructing distribution-free confidence intervals for quantiles for finite populations. The required algorithms for computing coverage probabilities of the proposed confidence intervals are presented. The second problem we address is that of constructing nonparametric confidence intervals for infinite populations. We describe the procedures for constructing confidence intervals and compare the constructed confidence intervals in the RNS setting, both in perfect and imperfect ranking scenario, with their simple random sampling (SRS) counterparts. Recommendations for choosing the design parameters are made to achieve shorter confidence intervals than their SRS counterparts. The third problem we investigate is the construction of tolerance intervals using the RNS technique. We describe the procedures of constructing one- and two-sided RNS tolerance intervals and investigate the sample sizes required to achieve tolerance intervals which contain the determined proportions of the underlying population. We also investigate the efficiency of RNS-based tolerance intervals compared with their corresponding intervals based on SRS. A new method for estimating ranking error probabilities is proposed. The final problem we consider is that of parametric inference based on RNS. We introduce different data types associated with different situation that one might encounter using the RNS design and provide the maximum likelihood (ML) and the method of moments (MM) estimators of the parameters in two classes of distributions; proportional hazard rate (PHR) and proportional reverse hazard rate (PRHR) models.

The diploma thesis deals with the creation of loans provisions in banks. The need for adjustments is based on the existence of credit risk and this thesis presents techniques of credit risk measurement and applied credit risk indicators. Before calculating provisions, it is necessary to classify receivables, whose parameters are also discussed in the thesis. The practical part focuses on methods of calculating provisions. The method of coefficients, discounted cash flow method and statistical methods are compared. Markov model and gross roll rate model were selected from statistical methods. The findings were evaluated and recommendations were made based on the findings.

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無 / Existing literature has shown that force of mortality has amazing resemblance of interest rate. It is then tempting to extend existing model of interest rate model context to mortality modeling. We apply the model in Diebold and Li (2006) and other models that belong to family of yield rate model originally proposed by Nelson and Siegel (1987) to forecast (force of) mortality term structure. The fitting performance of extended Nelson-Siegel model is comparable to the benchmark Lee-Carter model. While forecasting performance is no better than Lee-Carter model in younger ages, it is at the same level in elder ages. The forecasting performance increases for 5-year ahead forecast is better than 1-year ahead comparing to Lee-Carter forecast. In the end, the forecast outperforms Lee-Carter model when age dimension is trimmed to age 20-100.

In this thesis we propose models based on a reparameterized Birnbaum-Saunder (BS) distribution introduced by Santos-Neto et al. (2012) and Santos-Neto et al. (2014), to analyze survival data. Initially we introduce the Birnbaum-Saunders frailty model where we analyze the cases (i) with (ii) without covariates. Survival models with frailty are used when further information is nonavailable to explain the occurrence time of a medical event. The random effect is the frailty, which is introduced on the baseline hazard rate to control the unobservable heterogeneity of the patients. We use the maximum likelihood method to estimate the model parameters. We evaluate the performance of the estimators under different percentage of censured observations by a Monte Carlo study. Furthermore, we introduce a Birnbaum-Saunders regression frailty model where the maximum likelihood estimation of the model parameters with censored data as well as influence diagnostics for the new regression model are investigated. In the following we propose a cure rate Birnbaum-Saunders frailty model. An important advantage of this proposed model is the possibility to jointly consider the heterogeneity among patients by their frailties and the presence of a cured fraction of them. We consider likelihood-based methods to estimate the model parameters and to derive influence diagnostics for the model. In addition, we introduce a bivariate Birnbaum-Saunders distribution based on a parameterization of the Birnbaum-Saunders which has the mean as one of its parameters. We discuss the maximum likelihood estimation of the model parameters and show that these estimators can be obtained by solving non-linear equations. We then derive a regression model based on the proposed bivariate Birnbaum-Saunders distribution, which permits us to model data in their original scale. A simulation study is carried out to evaluate the performance of the maximum likelihood estimators. Finally, examples with real-data are performed to illustrate all the models proposed here. / Nesta tese propomos modelos baseados na distribuição Birnbaum-Saunders reparametrizada introduzida por Santos-Neto et al. (2012) e Santos-Neto et al. (2014), para análise dados de sobrevivência. Inicialmente propomos o modelo de fragilidade Birnbaum-Saunders sem e com covariáveis observáveis. O modelo de fragilidade é caracterizado pela utilização de um efeito aleatório, ou seja, de uma variável aleatória não observável, que representa as informações que não podem ou não foram observadas tais como fatores ambientais ou genéticos, como também, informações que, por algum motivo, não foram consideradas no planejamento do estudo. O efeito aleatório (a fragilidade) é introduzido na função de risco de base para controlar a heterogeneidade não observável. Usamos o método de máxima verossimilhança para estimar os parâmetros do modelo. Avaliamos o desempenho dos estimadores sob diferentes percentuais de censura via estudo de simulações de Monte Carlo. Considerando variáveis regressoras, derivamos medidas de diagnóstico de influência. Os métodos de diagnóstico têm sido ferramentas importantes na análise de regressão para detectar anomalias, tais como quebra das pressuposições nos erros, presença de outliers e observações influentes. Em seguida propomos o modelo de fração de cura com fragilidade Birnbaum-Saunders. Os modelos para dados de sobrevivência com proporção de curados (também conhecidos como modelos de taxa de cura ou modelos de sobrevivência com longa duração) têm sido amplamente estudados. Uma vantagem importante do modelo proposto é a possibilidade de considerar conjuntamente a heterogeneidade entre os pacientes por suas fragilidades e a presença de uma fração curada. As estimativas dos parâmetros do modelo foram obtidas via máxima verossimilhança, medidas de influência e diagnóstico foram desenvolvidas para o modelo proposto. Por fim, avaliamos a distribuição bivariada Birnbaum-Saunders baseada na média, como também introduzimos um modelo de regressão para o modelo proposto. Utilizamos os métodos de máxima verossimilhança e método dos momentos modificados, para estimar os parâmetros do modelo. Avaliamos o desempenho dos estimadores via estudo de simulações de Monte Carlo. Aplicações a conjuntos de dados reais ilustram as potencialidades dos modelos abordados.

Neste trabalho são apresentadas algumas extensões de modelos de sobrevivência com fração de cura, assumindo o contexto em que as observações estão agrupadas. Dois efeitos aleatórios são incorporados para cada grupo: um para explicar o efeito no tempo de sobrevida das observações suscetíveis e outro para explicar a probabilidade de cura. Apresenta-se uma abordagem clássica através dos estimadores REML e uma abordagem bayesiana através do uso de processos de Dirichlet. Discute-se alguns estudos de simulação em que avalia-se o desempenho dos estimadores propostos, além de comparar as duas abordagens. Finalmente, ilustram-se os resultados com dados reais. / In this work some extensions in survival models with cure fraction are presented, assuming the context in which the observations are grouped into clusters. Two random effects are incorporated for each group: one to explain the effect on survival time of susceptible observations and another to explain the probability of cure. A classical approach through the REML estimators is presented as well as a bayesian approach through Dirichlet Process. Besides comparing both approaches, some simulation studies which evaluates the performance of the proposed estimators are discussed. Finally, the results are illustrated with a real database.

The demographic structure seems to change dramatically over the next 50 years in the Czech Republic. The aim of this study is to assess the impact of expected demographic changes on the future development of a real interest rate and international capital flows. In order to simulate the impact of the expected demographic changes upon the mentioned variables we apply a computable overlapping generations model. The real interest rate development is simulated under a closed economy assumption. As a result of the future expected demographic changes labour-capital ratio tends to fall, i.e. the real interest rate diminishes. The range of a change is significantly affected by a public budget closure rule. In case of an endogenous income tax rate, the real interest rate falls down by 0.5 percentage point. On the contrary, the real interest rate decreases by almost 1 percentage point in case when public transfers adjusted. Assuming an open economy, we simulate the impact of the expected demographic changes on the international capital flows between the domestic economy and the rest of the world. In case of increasing ratio of older agents, the aggregate domestic wealth surpasses the demand for capital by domestic firms. As a result a part of domestic capital is exported abroad. Increasing level of net foreign assets contributes to positive change in ratio of the balance of payment to the domestic production in a range from 2 to 5 percentage points over next 40 years if income taxes or public transfers change respectively.

Neste trabalho são apresentadas algumas extensões de modelos de sobrevivência com fração de cura, assumindo o contexto em que as observações estão agrupadas. Dois efeitos aleatórios são incorporados para cada grupo: um para explicar o efeito no tempo de sobrevida das observações suscetíveis e outro para explicar a probabilidade de cura. Apresenta-se uma abordagem clássica através dos estimadores REML e uma abordagem bayesiana através do uso de processos de Dirichlet. Discute-se alguns estudos de simulação em que avalia-se o desempenho dos estimadores propostos, além de comparar as duas abordagens. Finalmente, ilustram-se os resultados com dados reais. / In this work some extensions in survival models with cure fraction are presented, assuming the context in which the observations are grouped into clusters. Two random effects are incorporated for each group: one to explain the effect on survival time of susceptible observations and another to explain the probability of cure. A classical approach through the REML estimators is presented as well as a bayesian approach through Dirichlet Process. Besides comparing both approaches, some simulation studies which evaluates the performance of the proposed estimators are discussed. Finally, the results are illustrated with a real database.

In this thesis, we present two different approaches for the stochastic volatility and stochastic interest rate model with jump and analyze the performance of four alternative models. In the first approach, suggested by Scott, the closed form solution for prices on European call stock options are developed by deriving characteristic functions with the help of martingale methods. Here, we study the asset price process and give in detail the derivation of the European call option price process. The second approach, suggested by Bashki-Cao-Chen, describes the closed form solution of European call option by deriving the partial integro-differential equation. In this one we g ive the derivations of both asset price dynamics and the European call option price process. Finally, in the application part of the thesis, we examine the performance of four alternative models using General Electric Stock Option Data. These models are constructed by using the theoretical results of the second approach.

Magister Commercii - MCom / Issues pertaining to the misalignment of exchange rate have become central in the analysis of open economy macroeconomics for developing countries. This is at least due to two reasons: first persistent overvaluation of currency is seen as a powerful early warning of potential currency crisis and second protracted periods of exchange rate misalignment are highly associated with poor economic performance in a number of developing countries. Owing to this fact, economists are in concession that aligning real exchange rates towards their equilibrium values is an important component of macroeconomic policy adjustments in order to achieve and maintain a sustainable development. For this purpose the estimation of the degree of the real exchange rate misalignment has become pivotal. However, despite the concession among economists regarding the need to minimize the frequency and magnitude of exchange rate misalignment, the estimation of the equilibrium exchange rate (hence the misalignment) has been among the most controversial and challenging issues in modem macroeconomics. For several decades, the Purchasing power parity (PPP) approach-which is based on the law of one price-has been the most widely used methodology for the estimation of the equilibrium exchange rate in both developed and developing countries. In South Africa some attempts have been made to estimate the misalignment of the rand against major currencies on the basis of the PPP approach. However, large numbers of empirical studies show that PPP does not hold except in the 'ultra' long run. In addition, PPP's assumption of a constant equilibrium exchange rate makes it ill-fitted to serve as a bench-mark for the analysis of the exchange rate in countries such as South Africa that experience substantial structural changes. As a result a number of macro-econometric models underlying on the macroeconomic determinants of exchange rate have been developed, albeit with little applicability in developing countries. In this study, we have used Edwards' (1989) intertemporal general equilibrium model of a small open economy in order to estimate the degree of the real exchange rate misalignment and its impact on the international trade competitiveness of the South African economy for the period 1985:1-2000:4. For this purpose a dynamic single equation error correction model of a first order autoregressive distributed lag model, ADL (1,1), and five years moving average technique have been employed to estimate the exchange rate misalignment. Whereas impulse response analysis and variance decomposition techniques of a cointegrated VAR (vector auto regression) have been established to assess the impact of the misalignment on trade competitiveness. The fmdings of the study reveal that the real exchange rate had been consistently overvalued during the period' 1988:3-1998:2 but undervalued during periods 1998:3- 2000:4. For most of the periods during 1985:1-1988:2 the rand had been undervalued. More over the study discloses that exchange rate misalignment debilitates South Africa's international trade competitiveness accounting for 20 percent of the variation in competitiveness.