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Option pricing in market models driven by telegraph processes with jumps

Esta tesis está dividida en dos partes: en la primera parte se presentan y estudian los procesos telegráficos, los procesos de Poisson con compensador telegráfico y los procesos telegráficos con saltos. El estudio presentado en esta primera parte incluye el cálculo de las distribuciones de cada proceso, las medias y varianzas, así como las funciones generadoras de momentos entre otras propiedades. Utilizando estas propiedades en la segunda parte se estudian los modelos de valoración de opciones basados en procesos telegráficos con saltos. En esta parte se da una descripción de cómo calcular las medidas neutrales al riesgo, se encuentra la condición de no arbitraje en este tipo de modelos y por último se calcula el precio de las opciones Europeas de compra y venta.

Extending Zelterman’s approach for robust estimation of population size to zero-truncated clustered data

Estimation of population size with missing zero-class is an important problem that is encountered in epidemiological assessment studies. Fitting a Poisson model to the observed data by the method of maximum likelihood and estimation of the population size based on this fit is an approach that has been widely used for this purpose. In practice, however, the Poisson assumption is seldom satisfied. Zelterman (1988) has proposed a robust estimator for unclustered data that works well in a wide class of distributions applicable for count data. In the work presented here, we extend this estimator to clustered data. The estimator requires fitting a zero-truncated homogeneous Poisson model by maximum likelihood and thereby using a Horvitz-Thompson estimator of population size. This was found to work well, when the data follow the hypothesized homogeneous Poisson model. However, when the true distribution deviates from the hypothesized model, the population size was found to be underestimated. In the search of a more robust estimator, we focused on three models that use all clusters with exactly one case, those clusters with exactly two cases and those with exactly three cases to estimate the probability of the zero-class and thereby use data collected on all the clusters in the Horvitz-Thompson estimator of population size. Loss in efficiency associated with gain in robustness was examined based on a simulation study. As a trade-off between gain in robustness and loss in efficiency, the model that uses data collected on clusters with at most three cases to estimate the probability of the zero-class was found to be preferred in general. In applications, we recommend obtaining estimates from all three models and making a choice considering the estimates from the three models, robustness and the loss in efficiency. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

Use of the ratio plot in capture-recapture estimation

Statistical graphics are a fundamental, yet often overlooked, set of components in the repertoire of data analytic tools. Graphs are quick and efficient, yet simple instruments of preliminary exploration of a dataset to understand its structure and to provide insight into influential aspects of inference such as departures from assumptions and latent patterns. In this paper, we present and assess a graphical device for choosing a method for estimating population size in capture-recapture studies of closed populations. The basic concept is derived from a homogeneous Poisson distribution where the ratios of neighboring Poisson probabilities multiplied by the value of the larger neighbor count are constant. This property extends to the zero-truncated Poisson distribution which is of fundamental importance in capture–recapture studies. In practice however, this distributional property is often violated. The graphical device developed here, the ratio plot, can be used for assessing specific departures from a Poisson distribution. For example, simple contaminations of an otherwise homogeneous Poisson model can be easily detected and a robust estimator for the population size can be suggested. Several robust estimators are developed and a simulation study is provided to give some guidance on which should be used in practice. More systematic departures can also easily be detected using the ratio plot. In this paper, the focus is on Gamma mixtures of the Poisson distribution which leads to a linear pattern (called structured heterogeneity) in the ratio plot. More generally, the paper shows that the ratio plot is monotone for arbitrary mixtures of power series densities.

Detecting regular sound changes in linguistics as events of concerted evolution

Background: Concerted evolution is normally used to describe parallel changes at different sites in a genome, but it is also observed in languages where a specific phoneme changes to the same other phoneme in many words in the lexicon—a phenomenon known as regular sound change. We develop a general statistical model that can detect concerted changes in aligned sequence data and apply it to study regular sound changes in the Turkic language family. Results: Linguistic evolution, unlike the genetic substitutional process, is dominated by events of concerted evolutionary change. Our model identified more than 70 historical events of regular sound change that occurred throughout the evolution of the Turkic language family, while simultaneously inferring a dated phylogenetic tree. Including regular sound changes yielded an approximately 4-fold improvement in the characterization of linguistic change over a simpler model of sporadic change, improved phylogenetic inference, and returned more reliable and plausible dates for events on the phylogenies. The historical timings of the concerted changes closely follow a Poisson process model, and the sound transition networks derived from our model mirror linguistic expectations. Conclusions: We demonstrate that a model with no prior knowledge of complex concerted or regular changes can nevertheless infer the historical timings and genealogical placements of events of concerted change from the signals left in contemporary data. Our model can be applied wherever discrete elements—such as genes, words, cultural trends, technologies, or morphological traits—can change in parallel within an organism or other evolving group.

Ensaios em opções reais e investimento sob incerteza

Esta tese é composta por três artigos, nos quais são apresentadas extensões e aplicações da Teoria das Opções Reais, todas de interesse para formuladores de política econômica no Brasil. O primeiro faz uma análise original da questão da bioprospecção, ou a exploração da diversidade biológica para fins econômicos. Duas estruturas alternativas para o desenho do mecanismo de concessão, visando o uso sustentável da biodiversidade brasileira, são sugeridas: (i) um modelo de projetos de P&D com maturidade incerta, no qual a intensidade do processo de Poisson que governa o tempo de maturação é explicitamente dependente do nível da biodiversidade no local concedido; (ii) um modelo de Agente-Principal, onde o Estado delega o exercício da opção de investimento à empresa de pesquisa biotecnológica. O segundo artigo avança a analogia entre opções de venda (“put options”) e cotas de importação. Os parâmetros relevantes para apreçar as licenças são agora obtidos endogenamente, a partir da interação entre a firma importadora e os produtores domésticos. Por fim, no terceiro, é feita análise pioneira do mercado paralelo de títulos precatórios no Brasil. Um modelo para a valoração de tais títulos é construído e proposto, tendo por base o arcabouço institucional existente sobre o assunto, tanto no governo central, como nos estados e municípios.

Controle on-line por atributos para o número de não-conformidades no item inspecionado com base em uma sequência de inspeção

This paper proposes a procedure to control on-line processes for attributes, using an Shewhart control chart with two control limits (warning limit and control limit) and will be based on a sequence of inspection (h). The inspection procedure is based on Taguchi et al. (1989), in which to inspect the item, if the number of non-conformities is higher than an upper control limit, the process needs to be stopped and some adjustment is required; and, if the last inspection h, from all items inspected present a number of non-conformities between the control limit and warning limit. The items inspected will suffer destructive inspection, being discarded after inspection. Properties of an ergodic Markov chain are used to get the expression of average cost per item and the aim was the determination of four optimized parameters: the sampling interval of the inspections (m); the constant W to draw the warning limit (W); the constant C to draw the control limit (C), where W £ C, and the length of sequence of inspections (h). Numerical examples illustrate the proposed procedure

Caracterização de látices acrílicos em função da neutralização de seus grupos carboxilas

Latexes based on acrylic acid, acrylamide, ethyl methacrylate, and ethyl acrylate were synthesized via emulsion polymerization with different monomer compositions. The resultant latices were thickened with different molar ratios of NaOH to acrylic acid and were analyzed in terms of acid‐basis titrimetry, turbidimetry, rheology, and tensiometry. Titrimetry, turbidimetry, and rheometry were used to analyze factors such as carboxyl group availability and particle solubilization, tensiometry monitoring the influence of carboxyl neutralization on polymer‐surfactant interactions. For the acrylic acid content used in this work (20 wt%), the results indicated that as carboxyl groups distribution became more homogeneous, the process of latex thickening became more effective

Colloidal particles: Spherical yttrium iron garnet

The purpose of this work is to obtain spherical particles YIG from micrometric to nanometric scales. The spherical particles were obtained from cation hydrolysis in acid medium by adding urea or ammonia in order to carry out a homogeneous nucleation process up to 90 degrees C. Different composition and morphology were achieved by changing reactant concentrations, precipitation agent and stabilizing agent. X-ray diffractometry, electrophoretic mobility, transmission and scanning electron microscopies were carried out on these particles to investigate the phase identification, mobility, morphology and particle size. Crystalline YIG, with spherical characteristics, was obtained. The surface potential presented different characteristics for different dispersion media.