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A Numerical Study of a Parabolic Monge-Ampère Equation in Mathematical Finance

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Book cover Numerical Methods and Applications (NMA 2010)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6046))

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Abstract

We propose iterative algorithms for solving finite difference schemes approximating an initial value problem of a parabolic Monge-Ampère equation, arising from the optimal investment of mathematical finance theory. We investigate positivity and convexity preserving properties of the numerical solution. Convergence results are also given. Numerical experiments demonstrate the efficiency of the algorithms and verify theoretical statements.

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Author information

Authors and Affiliations

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

    Miglena N. Koleva & Lubin G. Vulkov

Authors
  1. Miglena N. Koleva
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  2. Lubin G. Vulkov
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Editor information

Editors and Affiliations

  1. Institute of Computer and Communication Technologies, Bulgarian Academy of Sciences, Acad. G. Bonchev 25 A, 1113, Sofia, Bulgaria

    Ivan Dimov

  2. Faculty of Mathematics and Informatics, Department Numerical Methods and Algorithms, University of Sofia "St. Kliment Ohridski",, blvd. James Bourchier 5, 1164, Sofia, Bulgaria

    Stefka Dimova

  3. Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Acad. Bonchev St.,Bl.8, 1113, Sofia, Bulgaria

    Natalia Kolkovska

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© 2011 Springer-Verlag Berlin Heidelberg

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Koleva, M.N., Vulkov, L.G. (2011). A Numerical Study of a Parabolic Monge-Ampère Equation in Mathematical Finance. In: Dimov, I., Dimova, S., Kolkovska, N. (eds) Numerical Methods and Applications. NMA 2010. Lecture Notes in Computer Science, vol 6046. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-18466-6_55

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  • DOI: https://doi.org/10.1007/978-3-642-18466-6_55

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-18465-9

  • Online ISBN: 978-3-642-18466-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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