Modelos de Lévy de atividade infinita

Abstract

In this work, we present a class of pure jump Lévy processes A, with internal filtration and Itô-Lévy decomposition and we established an explicit forms for martingale representation, main component of our process. Furthermore, we propose an optimal Itô-Meyer formula for a Lévy functional and Euler-Maruyama approach scheme for a path-dependent SDE driven by A Lévy process. For that, first, we close A by a Poisson process composed of Ae , that we proved to converge strongly in B2 to A, when e ↓ 0. This result is fundamental to show that, given a supermartingale Snell envelope S, we can approach it through an imbedded discrete structure , which is the sequence of value processes, associated with S.