Modelos de Lévy de atividade infinita
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-...
| Autor: | |
|---|---|
| Tipo de recurso: | tesis doctoral |
| Estado: | Versión publicada |
| Fecha de publicación: | 2020 |
| País: | Brasil |
| Institución: | Universidade Federal de São Carlos (UFSCAR) |
| Repositorio: | Repositório Institucional da UFSCAR |
| Idioma: | portugués |
| OAI Identifier: | oai:repositorio.ufscar.br:20.500.14289/13138 |
| Acceso en línea: | https://repositorio.ufscar.br/handle/20.500.14289/13138 |
| Access Level: | acceso abierto |
| Palabra clave: | Processos de Lévy Martingale Fórmula de Itô Equações diferencias estocásticas Parada ótima Lévy processes Itô formula Stochastic differential equation Optimal stopping CIENCIAS EXATAS E DA TERRA::PROBABILIDADE E ESTATISTICA |
| Sumario: | 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. |
|---|