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ABSTRACT The aim of this paper is to investigate the use of close formula approximation for pricing European mortgage options. Under the assumption of logistic duration and normal mortgage rates the underlying price at the option expiry is approximated by shifted lognormal or regular lognormal distribution by matching moments. Once the price function is approximated by lognormal distributions, the option price can be computed directly as an integration of the distribution function over the payoff at the option expiry by using Black-Scholes-Merton close formula. We will see that lower curvature levels correspond to positively skewness price distributions and in this case lognormal approximation leads to close parametric formula representation in terms of all model parameters. The proposed methodologies are tested against Monte Carlo approach under different market and contract parameters and the tests confirmed that the close form approximation have a very good accuracy.Resumo em Português:
RESUMO Neste trabalho, apresentamos um modelo geral para selecionar carteiras de investimento a partir da maximização de um momento ímpar de ordem superior quando fixados os dois primeiros momentos, considerando um ativo livre de risco e permitindo vendas a descoberto. Deduzimos propriedades geométricas de suas soluções. Propomos ainda uma generalização ao modelo Média-variância de Markowitz, pela minimização de um momento par de ordem superior sujeita a um retorno fixo.Resumo em Inglês:
ABSTRACT This paper presents a general model to portfolio selection based on maximizing a higher-order odd moment when the first two moments are fixed, considering a risk- free asset, and allowing short sales. We deduce geometric properties from their solutions and also propose a generalization to the Markowitz Mean-Variance model by minimizing a higher-order even moment subject to a fixed return.Resumo em Inglês:
ABSTRACT This work presents a combinatorial bijection between the set of lattice paths and the set of ordered trees, both counted by the central coefficients of the expansion of the trinomial (1 + x + x2)n. Moreover, using a combinatorial interpretation of Catalan numbers, we establish a new set of ordered trees counted by a new sequence.Resumo em Inglês:
ABSTRACT In this article a preconditioned version of the Delayed Weighted Gradient Method (DWGM) is presented and analyzed. In addition to the convergence, some nice properties as the A- orthogonality of the current transformed gradient with all the previous gradient vectors as well as finite convergence are demonstrated. Numerical experimentation is also offered, exposing the benefits of preconditioning.Resumo em Inglês:
ABSTRACT Development of mathematical models and its numerical implementations are essential tools in epidemiological modeling. Susceptible-Infected-Recovered (SIR) compartmental model, proposed by Kermack and McKendrick in 1927, is a widely used deterministic model which serves as a basis for more involved mathematical models. In this work, we consider two stochastic versions of the SIR model for analysing a measles outbreak in Ilha Grande, Rio de Janeiro, in 1976; Continuous Time Markov Chain and Stochastic Differential Equations. The SIR Continuous Time Markov Chain model is used to extract specific information from the measles outbreak. The outbreak probability, final size distribution and expected duration of the epidemic were computed, obtaining results in excellent agreement with the reported epidemic values. Numerical simulations are performed in Python.Resumo em Português:
RESUMO O crescimento do número de lançamentos de satélites artificiais para as mais diferentes funções tem motivado estudos relacionados a atividades de controle, propagação e determinação de órbita e atitude. Neste trabalho é feito um estudo do Torque de Pressão de Radiação Solar (TPRS) e do Torque Aerodinâmico (TA) do satélite CBERS (China-Brazil Earth Resources Satellite) quando são considerados os modelos utilizados na missão do satélite. Os resultados mostraram que para satélites em órbitas baixas terrestres (Low Earth Orbit-LEO), como no caso do CBERS, o TA tem efeitos mais relevantes na superfície do satélite do que o TPRS. Estes resultados poderão ser úteis para a supervisão e controle do satélite no pós-lançamento, sendo vital para o controle de atitude e da órbita do satélite CBERS.Resumo em Inglês:
ABSTRACT The growth in the number of launches of artificial satellites for the most different functions has motivated studies related to control, propagation, and orbit and attitude determination activities. In this paper a study of the Solar Radiation Pressure Torque (SRPT) and Aerodynamic Torque (AT) of the CBERS (China-Brazil Earth Resources Satellite) satellite is done when the models used in the satellite mission are considered. The results showed that for satellites in Low Earth Orbit (LEO), as in the case of CBERS, the AT has more relevant effects on the satellite’s superfıcie than the SRPT. These results could be useful for satellite supervision and control in post-launch, and are vital for attitude and orbit control of the CBERS satellite.Resumo em Inglês:
ABSTRACT In this contribution, we present a predictive tool developed to help in the management of the evolution of the COVID-19 pandemic situation in Rio Grande do Sul (RS)-Brazil. This tool is the result of georeferenced data analysis, mathematical modeling, and parameter calibration for the dynamics of a SIR-type model defined on a spatial structure that allows distinct subpopulations to interact, similar to the controlled distancing (A l for l=1, ···, 21)) groupings proposed by the RS government and public health authorities. The predictive analysis, updated biweekly, provides three distinct scenarios per month (milder, average, and severe) and is made available as WebSIGs (Geographic Information System-GIS). The forecast of the average scenario for each A l group is the result of a simulation of the proposed SIR-type dynamics with calibrated parameters derived from an augmented Lagrangian maximum a posteriori estimation and data on the number of infected cases made available by the RS Health Secretariat. The milder and severe scenarios are obtained from the average scenario, with changes in the contagion rates of each A l group. When compared to the number of infections reported in each A l group, the modeling predictions for a biweekly time window (the first two weeks) were quite satisfactory, with errors ranging from 0% to 5.13%, gradually increasing over time. Therefore, we suggest a biweekly re-calibration of the parameters and corresponding forecasts as a wise strategy.Resumo em Inglês:
ABSTRACT This work is concerned with the Cauchy problem for a Zakharov system with initial data in Sobolev spaces Hk(ℝd)×Hl(ℝd)×Hl-1(ℝd). We recall the well-posedness and ill-posedness results known to date and establish new ill-posedness results. We prove C 2 ill-posedness for some new indices (k,l)∈ℝ2. Moreover, our results are valid in arbitrary dimension. We believe that our detailed proofs are built on a methodical approach and can be adapted to obtain similar results for other systems and equations.Resumo em Inglês:
ABSTRACT Vector-borne diseases are a cause of concern all around the world, especially in Brazil. In the past few years, the Brazilian health system faced recurrent epidemics such as Dengue and Malaria as well as new cases of Chikungunya, Zika and Yellow Fever. Vector control continues to be one of the most important counter measures against these types of diseases. Mathematical models are important tools for planning vector control strategies. In this work we present an approach in order to calculate what is the minimum vector control intensity to obtain stability in a simple population’s dynamics model of mosquitoes. We combined numerical simulations with analytic results. Transcritical bifurcations appear in our analysis considering different control’s parameters values for the eggs, larvae, pupae and adults mosquitoes populations. A discussion about combined strategies of vector control was also showed.Resumo em Inglês:
ABSTRACT A flexible parametric mixture cure model, called bi-lognormal cure rate model or simply BLN model, is defined and studied. The BLN model can be effectively used to analyze survival dataset in the presence of long-term survivors, especially when the dataset presents the underlying phenomenon of latent competing risks or when there is evidence that a bimodal hazard function is appropriated to described it, which are advantages over other cure rate models found in the literature. We discuss the maximum likelihood estimation for the model parameters considering interval-censored data through the differential evolution algorithm that is a nature-inspired computing metaheuristic used for global optimization of functions defined in multidimensional spaces. This approach is also used because the likelihood function of the model is multimodal and the direct application of gradient methods in this case is not ideal, since such methods are local search methods with a high chance of getting stuck at a local maximum when the starting point is chosen outside the basin of attraction of a global maximum. In addition, a simulation study was implemented to compare the performance of differential evolution algorithm with the performance of the Newton-Raphson algorithm in terms of bias, root mean square error, and the coverage probability of the asymptotic confidence intervals for the parameters. Finally, an application of the BLN model to real data is presented to illustrate that it can provide a better fit than other mixture cure rate models.Resumo em Português:
RESUMO O objetivo desse artigo é a formação e a otimização de carteiras de investimento com ações negociadas na B3 e baseada na teoria de diversificação do modelo de Markowitz e na Programação Quadrática. Considerou-se a minimização do risco da carteira pelo sistema Downside Risk, modelado e implementado computacionalmente. O período de coleta de dados iniciou-se em 2020, ano em que houve uma crise econômica mundial em razão da pandemia da Sars-CoV-2 e consequentes medidas de isolamento que afetaram profundamente a economia. Foram formadas três carteiras que performaram entre Janeiro de 2021 a Março de 2022 e mostraram resultados acima do esperado em comparação à variação percentual do Ibovespa.Resumo em Inglês:
ABSTRACT Objective of this paper is the formation and optimization of investment portfolios with shares traded on B3 and based on the theory of diversification of the Markowitz model and on Quadratic Programming. The minimization of the portfolio risk was considered by the Downside Risk system, modeled and implemented computationally. The data collection period began in 2020, the year in which there was a global economic crisis due to the Sars-CoV-2 pandemic and consequent isolation measures that profoundly affected the economy. Three portfolios were formed that performed between January 2021 and March 2022 and showed better-than-expected results compared to the percentage change in the Ibovespa.Resumo em Inglês:
ABSTRACT An epidemiological model is proposed to analyze the COVID-19 epidemics when control interventions are being applied to reduce the speed of the disease. The analyzed model includes parameters that describe control strategies such as behavioral changes of susceptible individuals to reduce the transmission of the disease, rates of diagnosis of the infectious individuals, and other control measures as cleaning and disinfection of contaminated environments. The proposed model is calibrated using Bayesian statistics and the official cumulative confirmed cases for COVID-19 in Mexico. We show which public health strategies contribute the most to the variation of R 0. A central result is the fact that the peak of the epidemics can drastically be changed depending on the time when the control strategies are introduced.