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Newton-Based Solvers for Nonlinear PDEs in Finance

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Novel Methods in Computational Finance

Part of the book series: Mathematics in Industry ((TECMI,volume 25))

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Abstract

In this chapter, different Newton-based solvers are introduced to solve fully nonlinear PDEs generated from financial problems. The first one concentrates on solving the root-finding problem from the nonlinear system after applying the standard finite difference method with implicit scheme. The second one addresses to solve the deferred correction problem which is transformed from the original PDE. Different numerical experiments in terms of accuracy and efficiency are compared and some improvements using Newton-like methods are also discussed.

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Acknowledgements

The authors thank Prof. Matthias Ehrhardt, Dr. E. Jan W. ter Maten from Bergische Universität Wuppertal, Prof. Daniel Ševčovič from Comenius University Bratislava, Prof. Kevin Parrott and Dr. André Ribeiro from University of Greenwich, for the fruitful discussions.

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Authors and Affiliations

  1. Department of Mathematical Sciences, University of Greenwich, London, UK

    Shih-Hau Tan & Choi-Hong Lai

Authors
  1. Shih-Hau Tan
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  2. Choi-Hong Lai
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Correspondence to Shih-Hau Tan .

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Editors and Affiliations

  1. Lehrstuhl für Angewandte Mathematik/Numerische Analysis, Bergische Universität Wuppertal, Wuppertal, Germany

    Matthias Ehrhardt

  2. Lehrstuhl für Angewandte Mathematik/Numerische Analysis, Bergische Universität Wuppertal, Wuppertal, Germany

    Michael Günther

  3. Lehrstuhl für Angewandte Mathematik/Numerische Analysis, Bergische Universität Wuppertal, Wuppertal, Germany

    E. Jan W. ter Maten

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Tan, SH., Lai, CH. (2017). Newton-Based Solvers for Nonlinear PDEs in Finance. In: Ehrhardt, M., Günther, M., ter Maten, E. (eds) Novel Methods in Computational Finance. Mathematics in Industry(), vol 25. Springer, Cham. https://doi.org/10.1007/978-3-319-61282-9_12

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