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

B. Hofmann 1  and R. Krämer 1
  • 1 Faculty of Mathematics, Technical University Chemnitz, D-09107 Chemnitz, Germany. E-mails: hofmannb@mathematik.tu-chemnitz.de, rokra@mathematik.tu-chemnitz.de

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 L2 -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 L1 , 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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This journal presents original articles on the theory, numerics and applications of inverse and ill-posed problems. These inverse and ill-posed problems arise in mathematical physics and mathematical analysis, geophysics, acoustics, electrodynamics, tomography, medicine, ecology, financial mathematics etc. Articles on the construction and justification of new numerical algorithms of inverse problem solutions are also published.

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