Title:
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
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