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Positivity Preserving Numerical Method for Optimal Portfolio in a Power Utility Two-Dimensional Regime-Switching Model

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Numerical Methods and Applications (NMA 2018)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11189))

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Abstract

We consider a two-dimensional regime switching model with power utility function. The problem is a system of parabolic partial differential equations with non-linear gradient terms and weakly coupled by non-linear exponential terms. We establish lower bounds for the solutions and then we construct an adequate finite difference method, preserving the qualitative properties of the exact solution. Finally, we present and discuss numerical results.

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Acknowledgements

This research is supported by the Bulgarian National Science Fund under Project DN 12/4 “Advanced analytical and numerical methods for nonlinear differential equations with applications in finance and environmental pollution”, 2017.

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Authors and Affiliations

  1. University of Ruse, 8 Studentska str., 7017, Ruse, Bulgaria

    Miglena N. Koleva & Lubin G. Vulkov

Authors
  1. Miglena N. Koleva
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  2. Lubin G. Vulkov
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Correspondence to Miglena N. Koleva .

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Editors and Affiliations

  1. Sofia University “St. Kliment Ohridski”, Sofia, Bulgaria

    Geno Nikolov

  2. Bulgarian Academy of Sciences, Sofia, Bulgaria

    Natalia Kolkovska

  3. Bulgarian Academy of Sciences, Sofia, Bulgaria

    Krassimir Georgiev

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Koleva, M.N., Vulkov, L.G. (2019). Positivity Preserving Numerical Method for Optimal Portfolio in a Power Utility Two-Dimensional Regime-Switching Model. In: Nikolov, G., Kolkovska, N., Georgiev, K. (eds) Numerical Methods and Applications. NMA 2018. Lecture Notes in Computer Science(), vol 11189. Springer, Cham. https://doi.org/10.1007/978-3-030-10692-8_48

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  • DOI: https://doi.org/10.1007/978-3-030-10692-8_48

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-10691-1

  • Online ISBN: 978-3-030-10692-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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