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A Splitting Numerical Scheme for Non-linear Models of Mathematical Finance

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Large-Scale Scientific Computing (LSSC 2013)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8353))

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Abstract

We present and analyze a splitting numerical scheme for two non-linear models of mathematical finance. Each of the problems is split into two parts: a hyperbolic equation solved numerically by using a flux limiter technique and a parabolic equation computed by implicit-explicit finite difference scheme. We show that the presented splitting numerical schemes are convergent and positivity preserving. Numerical results are also discussed.

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Acknowledgements

This research was supported by the European Union under Grant Agreement number 304617 (FP7 Marie Curie Action Project Multi-ITN STRIKE - Novel Methods in Computational Finance) and the Bulgarian National Fund of Science under Project DID 02/37-2009.

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Authors and Affiliations

  1. Faculty of Natural Science and Education, University of Rousse, 8 Studentska Str., 7017, Rousse, Bulgaria

    Miglena N. Koleva & Lubin G. Vulkov

Authors
  1. Miglena N. Koleva
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  2. Lubin G. Vulkov
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Corresponding author

Correspondence to Miglena N. Koleva .

Editor information

Editors and Affiliations

  1. Inst. of Info. & Comm. Technologies, Bulgarian Academy of Sciences, Sofia, Bulgaria

    Ivan Lirkov

  2. Bulgarian Academy of Sciences, Sofia, Bulgaria

    Svetozar Margenov

  3. Dept. of Informatics and Mathematical Modell, Technical University of Denmark, Kongens Lyngby, Denmark

    Jerzy Waśniewski

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Koleva, M.N., Vulkov, L.G. (2014). A Splitting Numerical Scheme for Non-linear Models of Mathematical Finance. In: Lirkov, I., Margenov, S., Waśniewski, J. (eds) Large-Scale Scientific Computing. LSSC 2013. Lecture Notes in Computer Science(), vol 8353. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-43880-0_69

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  • DOI: https://doi.org/10.1007/978-3-662-43880-0_69

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-43879-4

  • Online ISBN: 978-3-662-43880-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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