Nonparametric estimation for Levy processes with a view towards mathematical finance
| dc.creator | Figueroa-Lopez, Enrique | |
| dc.creator | Houdre, Christian | |
| dc.date | 2004-12-17 | |
| dc.date.accessioned | 2026-07-07T08:06:37Z | |
| dc.date.available | 2026-07-07T08:06:37Z | |
| dc.description | Nonparametric methods for the estimation of the Levy density of a Levy process are developed. Estimators that can be written in terms of the ``jumps'' of the process are introduced, and so are discrete-data based approximations. A model selection approach made up of two steps is investigated. The first step consists in the selection of a good estimator from a linear model of proposed Levy densities, while the second is a data-driven selection of a linear model among a given collection of linear models. By providing lower bounds for the minimax risk of estimation over Besov Levy densities, our estimators are shown to achieve the ``best'' rate of convergence. A numerical study for the case of histogram estimators and for variance Gamma processes, models of key importance in risky asset price modeling driven by Levy processes, is presented. | |
| dc.description | 68 pages, 19 figures, submitted to Annals of Statistics | |
| dc.identifier | https://arxiv.org/abs/math/0412351 | |
| dc.identifier | http://arxiv.org/abs/math/0412351 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/130670 | |
| dc.subject | Statistics Theory | |
| dc.subject | Probability | |
| dc.subject | 62G05 (primary); 60G51 (secondary) | |
| dc.title | Nonparametric estimation for Levy processes with a view towards mathematical finance | |
| dc.type | text |