Nonparametric estimation of Levy processes with a view towards mathematical finance

dc.contributor.advisor Houdré, Christian
dc.contributor.author Figueroa-Lopez, Jose Enrique en_US
dc.contributor.committeeMember Marcus C. Spruill
dc.contributor.committeeMember Richard Serfozo
dc.contributor.committeeMember Kertz, Robert P.
dc.contributor.committeeMember Shijie Deng
dc.contributor.department Mathematics en_US
dc.date.accessioned 2005-03-03T22:13:01Z
dc.date.available 2005-03-03T22:13:01Z
dc.date.issued 2004-04-08 en_US
dc.description.abstract Model selection methods and nonparametric estimation of Levy densities are presented. The estimation relies on the properties of Levy processes for small time spans, on the nature of the jumps of the process, and on methods of estimation for spatial Poisson processes. Given a linear space S of possible Levy densities, an asymptotically unbiased estimator for the orthogonal projection of the Levy density onto S is found. It is proved that the expected standard error of the proposed estimator realizes the smallest possible distance between the true Levy density and the linear space S as the frequency of the data increases and as the sampling time period gets longer. Also, we develop data-driven methods to select a model among a collection of models. The method is designed to approximately realize the best trade-off between the error of estimation within the model and the distance between the model and the unknown Levy density. As a result of this approach and of concentration inequalities for Poisson functionals, we obtain Oracles inequalities that guarantee us to reach the best expected error (using projection estimators) up to a constant. Numerical results are presented for the case of histogram estimators and variance Gamma processes. To calibrate parametric models,a nonparametric estimation method with least-squares errors is studied. Comparison with maximum likelihood estimation is provided. On a separate problem, we review the theoretical properties of temepered stable processes, a class of processes with potential great use in Mathematical Finance. en_US
dc.description.degree Ph.D. en_US
dc.format.extent 525455 bytes
dc.format.mimetype application/pdf
dc.identifier.uri http://hdl.handle.net/1853/5261
dc.language.iso en_US
dc.publisher Georgia Institute of Technology en_US
dc.subject Asset price models driven by Levy processes en_US
dc.subject Calibration
dc.subject Minimum contrast estimation
dc.subject Oracle inequalities
dc.subject Levy processes
dc.subject Nonparmetric estimation
dc.title Nonparametric estimation of Levy processes with a view towards mathematical finance en_US
dc.type Text
dc.type.genre Dissertation
dspace.entity.type Publication
local.contributor.advisor Houdré, Christian
local.contributor.corporatename College of Sciences
local.contributor.corporatename School of Mathematics
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relation.isOrgUnitOfPublication 84e5d930-8c17-4e24-96cc-63f5ab63da69
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