Research Reports

In this work we introduce Heath-Jarrow-Morton (HJM) interest rate models driven by fractional Brownian motions. By using support arguments we prove that the resulting model is arbitrage-free under proportional transaction costs in the same spirit of Guasoni et al [20, 21, 22]. In particular, we obtain a drift condition which is similar in nature to the classical HJM no-arbitrage drift restriction. The second part of this paper deals with consistency problems related to the fractional HJM dynamics. We give a fairly complete characterization of finitedimensional invariant manifolds for HJM models with fractional Brownian motion by means of Nagumo-type conditions. As an application, we investigate consistency of Nelson-Siegel family with respect to Ho-Lee and Hull-White models. It turns out that similar to the Brownian case such family does not go well with the fractional HJM dynamics with deterministic volatility. In fact, there is no nontrivial fractional interest rate model consistent with the Nelson-Siegel family.

rp-2008-12.pdf

We show that under quite general distributional conditions the asymptotic distribution of Hotteling's $T^2$ statistic is the chi-square distribution, which is also the asymptotic distribution of $T^2$ under the assumption of normality.

rp-2008-10.pdf

We address the question of detecting fingerprints of rhythm in written texts. We study texts from 20th century Brazilian and Portuguese authors. In these texts we codify the syllables according to whether they carry main stress or not, and whether they are at the beginning of a phonological word or not. Additionally, periods are also marked. Modeling the sequences of symbols obtained with this codification as Variable Length Markov Chains, we estimate the patterns for each text. This probabilistic model discriminates European Portuguese from Brazilian Portuguese. Moreover, the model obtained for each language has a clear linguistic interpretation, as it captures structural features which have long been conjectured in the literature.address the question of detecting fingerprints of rhythm in written texts. We study texts from 20th century Brazilian and Portuguese authors. In these texts we codify the syllables according to whether they carry main stress or not, and whether they are at the beginning of a phonological word or not. Additionally, periods are also marked. Modeling the sequences of symbols obtained with this codification as Variable Length Markov Chains, we estimate the patterns for each text. This probabilistic model discriminates European Portuguese from Brazilian Portuguese. Moreover, the model obtained for each language has a clear linguistic interpretation, as it captures structural features which have long been conjectured in the literature.

rp-2008-8.pdf

Utilizando métodos de cálculo diferencial e integral fracionários são apresentados e discutidos dois modos distintos de se calcular a função de Green, associada ao caso unidimensional, da assimchamada equação do telégrafo fracionária. Esta é uma equação diferencial parcial com coeficientes constantes e é resolvida através da metodologia da justaposição das transformadas de Fourier, na parte espacial, e Laplace, na parte temporal. Utilizando manipulações algébricas, i.e., efetuando os cálculos de um modo alternativo, obtemos uma outra expressão para a função de Green, num particular caso, ou seja, a solução é dada de uma outra maneira. Através da comparação entre os resultados obtidos a partir das duas maneiras, são obtidas novas relações e um teorema de adição para as funções deMittag-Leffler. É apresentada uma demonstração formal do teorema assim obtido e casos particulares do mesmo são discutidos.