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Numerical Treatment to a Non-local Parabolic Free Boundary Problem Arising in Financial Bubbles

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Abstract

In this paper, we continue to study a non-local free boundary problem arising in financial bubbles. We focus on the parabolic counterpart of the bubble problem and suggest an iterative algorithm which consists of a sequence of parabolic obstacle problems at each step to be solved, that in turn gives the next obstacle function in the iteration. The convergence of the proposed algorithm is proved. Moreover, we consider the finite difference scheme for this algorithm and obtain its convergence. At the end of the paper, we present and discuss computational results.

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Acknowledgements

This publication was made possible by NPRP Grant NPRP 5-088-1-021 from the Qatar National Research Fund (a member of Qatar Foundation). The statements made herein are solely the responsibility of the authors.

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Authors and Affiliations

  1. Institute of Mathematics, NAS of Armenia, 0019, Yerevan, Armenia

    Avetik Arakelyan

  2. Institute of Mathematics, NAS of Armenia, American University of Armenia, 0019, Yerevan, Armenia

    Rafayel Barkhudaryan

  3. Department of Mathematics, The Royal Institute of Technology, 100 44, Stockholm, Sweden

    Henrik Shahgholian

  4. Department of Mathematics, Statistics and Physics, Qatar University, P.O. Box 2713, Doha, Qatar

    Mohammad Salehi

Authors
  1. Avetik Arakelyan
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  2. Rafayel Barkhudaryan
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  3. Henrik Shahgholian
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  4. Mohammad Salehi
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Corresponding author

Correspondence to Rafayel Barkhudaryan.

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Communicated by Asadollah Aghajani.

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Arakelyan, A., Barkhudaryan, R., Shahgholian, H. et al. Numerical Treatment to a Non-local Parabolic Free Boundary Problem Arising in Financial Bubbles. Bull. Iran. Math. Soc. 45, 59–73 (2019). https://doi.org/10.1007/s41980-018-0119-5

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  • DOI: https://doi.org/10.1007/s41980-018-0119-5

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