CEMAPRE - Capítulos / Artigos em Livros Internacionais / Chapters in International Works
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- Mathematical models in financePublication . Grossinho, Maria do RosárioIn this paper we illustrate the interplay between Mathematics and Finance, pointing out the relevance of stochastic calculus and mathematical modelling in some important aspects of modern finance. We present two types of mathematical models: the binomial asset pricing model and continuous-time models. We point out some sensitive points of research.
- An overview of some mathematical models of blood rheologyPublication . Sequeira, Adélia; Janela, JoãoExperimental investigations over many years reveal that blood flow exhibits non-Newtonian characteristics such as shear-thinning, viscoelasticity and thixotropic behaviour. The complex rheology of blood is influenced by numerous factors including plasma viscosity, rate of shear, hematocrit, level of erythrocytes aggregation and deformability. Hemodynamic analysis of blood flow in vascular beds and prosthetic devices requires the rheological behaviour of blood to be characterized through appropriate constitutive equations relating the stress to deformation and rate of deformation. The objective of this paper is to present a short overview of some macroscopic constitutive models that can mathematically characterize the rheology of blood and describe its known phenomenological properties. Some numerical simulations obtained in geometrically reconstructed real vessels will be also presented to illustrate the hemodynamic behaviour using Newtonian and non-Newtonian inelastic models under a given set of physiological flow conditions.
- Financial econometric modelPublication . Nicolau, JoãoFour recent financial econometric models are discussed. The first aims to capture the volatility created by “chartists”; the second intends to model bounded random walks; the third involves a mechanism where the stationarity is volatility-induced, and the last one accommodates nonstationary diffusion integrated stochastic processes that can be made stationary by differencing.
- Polygonal billiards with a contractive reflection law: a review of some hyperbolic propertiesPublication . Del Magno, Gianluigi; Dias, João Lopes; Duarte, Pedro; Gaivão, José Pedro; Pinheiro, DiogoWe provide an overview of recent results concerning the dynamics of polygonal billiards with a contractive reflection law.
- Comparing parametric and semiparametric binary response modelsPublication . Proença, IsabelBinary response models are frequently applied in economics and other social sciences. Whereas standard parametric models such as Probit and Logit models still dominate the applied literature, there have been important theoretical advances in semi- and nonparametric approaches to binary response analysis (see Horowitz, 1993a, for an excellent and up-to-date survey). From the perspective of the applied researcher, the development of new techniques that go beyond Logit and Probit are important for several reasons: 1. Economic theory usually does not provide clear guidelines on how a parametric model should be specified. Hence, the assumptions underlying Probit and Logit models are rarely justified on theoretical grounds. Rather, they are motivated by convenience and by reference to “standard practice.” 2. Misspecification of parametric models can cause parameter estimates and inferences based on these parameters to be inconsistent. Moreover, predictions made from misspecified parametric models can be inaccurate and misleading.
- Interactive Graphics for teaching Simple StatisticsPublication . Proença, IsabelThe progress of computer science, in association with the progress of computer hardware, is making computers a more accessible and important tool in assisting individuals in processing and computing information. This fact enhances the use of computers for educational and teaching purposes. That is, the current sophisticated potential of computers can be used to provide a means to acquire concepts and to develop reasoning and problem-solving skills. Computer-aided learning (CAL) and computer-aided instruction (CAI) have become established fields in computer science; they utilize the computer as a tool for learning and presenting instruction that is individualized, interactive, and guided.
- A simple deconvolving Kernel density estimator when noise is GaussianPublication . Proença, IsabelDeconvolving kernel estimators when noise is Gaussian entail heavy calculations. In order to obtain the density estimates numerical evaluation of a specific integral is needed. This work proposes an approximation to the deconvolving kernel which simplifies considerably calculations by avoiding the typical numerical integration. Simulations included indicate that the lost in performance relatively to the true deconvolving kernel, is almost negligible in finite samples
- Analytical and numerical results for American style of perpetual put options through transformation into nonlinear stationary Black-Scholes equationsPublication . Grossinho, Maria do Rosário; Faghan, Yaser; Ševčovič, DanielWe analyze and calculate the early exercise boundary for a class of stationary generalized Black- Scholes equations in which the volatility function depends on the second derivative of the option price itself. A motivation for studying the nonlinear Black Scholes equation with a nonlinear volatility arises from option pricing models including, e.g., non-zero transaction costs, investors preferences, feedback and illiquid markets effects and risk from unprotected portfolio. We present a method how to transform the problem of American style of perpetual put options into a solution of an ordinary differential equation and implicit equation for the free boundary position. We finally present results of numerical approximation of the early exercise boundary, option price and their dependence on model parameters.
- Homoclinic and periodic solutions for a class of second order differential equationsPublication . Grossinho, Maria do Rosário; Minhós, F.; Tersian, S. A.In this paper we are concerned with the existence of positive homoclinic solutions of the second order equation …
- On the behavior of some estimators for the index of stabilityPublication . Crato, Nuno; Dowling-DaCosta, LeslieHeavy-tailed distributions have been used to model phenomena in which extreme events occur with high probability. In these type of occurrences, it is likely that extreme events are not observable after a certain threshold. Appropriate estimators are needed to deal with this type of truncated data. By means of simulation, it is shown that the well-known Hill-Hall estimator yields highly biased estimates in the presence of truncated data. An unbiased modified maximum likelihood estimator and the tail regression estimator are studied. The expected value and variance of the estimators is assessed in the cases of stable- and Pareto-distributed data.