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Journal of Inverse and Ill-posed Problems

Editor-in-Chief: Kabanikhin, Sergey I.


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1569-3945
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Volume 13, Issue 1

Issues

On maximum entropy regularization for a specific inverse problem of option pricing

B. Hofmann
  • Faculty of Mathematics, Technical University Chemnitz, D-09107 Chemnitz, Germany. E-mails: ,
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
/ R. Krämer
  • Faculty of Mathematics, Technical University Chemnitz, D-09107 Chemnitz, Germany. E-mails: ,
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar

We investigate the applicability of the method of maximum entropy regularization (MER) to a specific nonlinear ill-posed inverse problem (SIP) in a purely time-dependent model of option pricing, introduced and analyzed for an L 2 -setting in [9]. In order to include the identification of volatility functions with a weak pole, we extend the results of [12, 13], concerning convergence and convergence rates of regularized solutions in L 1 , in some details. Numerical case studies illustrate the chances and limitations of (MER) versus Tikhonov regularization (TR) for smooth solutions and solutions with a sharp peak. A particular paragraph is devoted to the singular case of at-the-money options, where derivatives of the forward operator degenerate.

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Published in Print: 2005-01-01


Citation Information: Journal of Inverse and Ill-posed Problems jiip, Volume 13, Issue 1, Pages 41–63, ISSN (Online) 1569-3953, ISSN (Print) 0928-0219, DOI: https://doi.org/10.1515/1569394053583739.

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[12]
R. Krämer and P. Mathé
Journal of Inverse and Ill-posed Problems, 2008, Volume 16, Number 5
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B Hofmann, B Kaltenbacher, C Pöschl, and O Scherzer
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[17]
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