Title:
Nonparametric estimation for Levy processes with a view towards mathematical finance
Nonparametric estimation for Levy processes with a view towards mathematical finance
dc.contributor.author | Figueroa-Lopez, Enrique | |
dc.contributor.author | Houdré, Christian | |
dc.contributor.corporatename | Georgia Institute of Technology. School of Mathematics | |
dc.contributor.corporatename | Purdue University. Dept. of Mathematics | |
dc.contributor.corporatename | Laboratoire d’ Analyse et de Mathématiques Appliquées | |
dc.date.accessioned | 2009-12-03T20:44:53Z | |
dc.date.available | 2009-12-03T20:44:53Z | |
dc.date.issued | 2004-11 | |
dc.description | AMS Subject Classification (2000): 62G05, 62P05, 60G51, 60E07 | en |
dc.description.abstract | Nonparametric methods for the estimation of the Levy density of a Levy process X are developed. Estimators that can be written in terms of the "jumps" of X 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. | en |
dc.description.sponsorship | NSF and NSA grants | en |
dc.identifier.uri | http://hdl.handle.net/1853/31261 | |
dc.language.iso | en_US | en |
dc.publisher | Georgia Institute of Technology | en |
dc.relation.ispartofseries | SOM1104-001 | en |
dc.subject | Levy processes | en |
dc.subject | Poisson processes | en |
dc.subject | Nonparametric estimation | en |
dc.subject | Minimum contrast estimators | en |
dc.subject | Penalized projection estimators | en |
dc.subject | Model selection | en |
dc.subject | Oracle inequalities | en |
dc.subject | Minimax risk on Besov spaces | en |
dc.subject | Adaptive estimation | en |
dc.subject | Variance Gamma process | en |
dc.title | Nonparametric estimation for Levy processes with a view towards mathematical finance | en |
dc.type | Text | |
dc.type.genre | Pre-print | |
dspace.entity.type | Publication | |
local.contributor.author | Houdré, Christian | |
local.contributor.corporatename | College of Sciences | |
local.contributor.corporatename | School of Mathematics | |
relation.isAuthorOfPublication | 1fcd2323-5c4e-4e86-92a2-574f8decf21e | |
relation.isOrgUnitOfPublication | 85042be6-2d68-4e07-b384-e1f908fae48a | |
relation.isOrgUnitOfPublication | 84e5d930-8c17-4e24-96cc-63f5ab63da69 |