Contributions to the problems of classification, regression and study of an inverse problem in finance

Abstract : We focus on the problems of regression, classification and an inverse problem in finance. We first deal with the regression on a random design problem, with a design taking its values in a Euclidean space and whose distribution admits a density. We prove the optimality of the estimator obtained by localized projections onto a multi-resolution analysis. We then turn to the supervised binary classification problem and prove that the plug-in classifier built upon the above procedure is optimal. Interestingly enough, it is computationally more efficient than alternative plug-in classifiers, which turns out to be a crucial feature in many practical applications. We then focus on the regression on a random design problem, with a design uniformly distributed on the hyper sphere of a Euclidean space. We show how the tight frame of needlets allows to transpose the traditional wavelet regression methods to this new setting. We finally consider the problem of recovering the risk-neutral density from quoted option prices. We show that the singular value decomposition of restricted call and put operators can be computed explicitly and used to tailor a simple quadratic program, which allows to recover a stable estimate of the risk-neutral density.
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Contributor : Jean-Baptiste Monnier <>
Submitted on : Monday, December 12, 2011 - 2:52:37 PM
Last modification on : Thursday, March 21, 2019 - 2:16:41 PM
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Jean-Baptiste Monnier. Contributions to the problems of classification, regression and study of an inverse problem in finance. Statistics [math.ST]. Université Paris-Diderot - Paris VII, 2011. English. ⟨tel-00650930⟩

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