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Numerical Treatment to a Non-local Parabolic Free Boundary Problem Arising in Financial Bubbles
NAS Armenia, Inst Math, Yerevan 0019, Armenia..
Amer Univ Armenia, Inst Math, NAS Armenia, Yerevan 0019, Armenia..
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).ORCID iD: 0000-0002-1316-7913
Qatar Univ, Dept Math Stat & Phys, POB 2713, Doha, Qatar..
2019 (English)In: Bulletin of the Iranian Mathematical Society, ISSN 1018-6301, E-ISSN 1017-060X, Vol. 45, no 1, p. 59-73Article in journal (Refereed) Published
Abstract [en]

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.

Place, publisher, year, edition, pages
Springer, 2019. Vol. 45, no 1, p. 59-73
Keywords [en]
Finite difference method, Viscosity solution, Free boundaries, Obstacle problem, Black-Scholes equation
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-245934DOI: 10.1007/s41980-018-0119-5ISI: 000459196900005Scopus ID: 2-s2.0-85061674630OAI: oai:DiVA.org:kth-245934DiVA, id: diva2:1296355
Note

QC 20190315

Available from: 2019-03-15 Created: 2019-03-15 Last updated: 2019-03-15Bibliographically approved

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Shahgholian, Henrik

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