A fully nonlinear problem arising in financial modelling

A fully nonlinear problem arising in financial modelling

We state existence and localisation results for a fully nonlinear boundary value problem using the upper and lower solutions method. With this study we aim to contribute to a better understanding of some analytical features of a problem arising in financial modelling related to the introduction of t...

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Published in:Boundary value problems Vol. 2013; no. 1; p. 146
Main Authors: Grossinho, Maria do Rosário, Morais, Eva
Format: Journal Article
Language:English
Published: Cham Springer International Publishing 13-06-2013
BioMed Central Ltd
Subjects:
Analysis
Approximations and Expansions
Difference and Functional Equations
Jean Mawhin's Achievements in Nonlinear Analysis
Mathematics
Mathematics and Statistics
Ordinary Differential Equations
Partial Differential Equations
Transaction Cost
Underlying Asset
Auxiliary Problem
Solution Versus
Option Price
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Abstract We state existence and localisation results for a fully nonlinear boundary value problem using the upper and lower solutions method. With this study we aim to contribute to a better understanding of some analytical features of a problem arising in financial modelling related to the introduction of transaction costs in the classical Black-Scholes model. Our result concerns stationary solutions which become interesting in finance when the time does not play a relevant role such as, for instance, in perpetual options.
AbstractList We state existence and localisation results for a fully nonlinear boundary value problem using the upper and lower solutions method. With this study we aim to contribute to a better understanding of some analytical features of a problem arising in financial modelling related to the introduction of transaction costs in the classical Black-Scholes model. Our result concerns stationary solutions which become interesting in finance when the time does not play a relevant role such as, for instance, in perpetual options.
ArticleNumber 146
Author Grossinho, Maria do Rosário
Morais, Eva
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  givenname: Eva
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  organization: ISEG, CEMAPRE - Technical University of Lisbon, Department of Mathematics, University of Trás-os-Montes e Alto Douro
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Cites_doi 10.1111/j.1540-6261.1985.tb02383.x
10.1016/j.jmaa.2004.08.067
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Copyright Grossinho and Morais; licensee Springer. 2013. This article is published under license to BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons Attribution License ( ), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Copyright_xml – notice: Grossinho and Morais; licensee Springer. 2013. This article is published under license to BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons Attribution License ( ), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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Issue 1
Keywords Transaction Cost
Underlying Asset
Auxiliary Problem
Solution Versus
Option Price
Language English
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Amster, Averbuj, Mariani, Rial (CR3) 2005; 303
Grossinho, Morais (CR4) 2009; 51
De Coster, Habets (CR2) 2006
Mawhin (CR1) 1985
Kabanov, Safarian (CR6) 2009
C De Coster (403_CR2) 2006
J Mawhin (403_CR1) 1985
MR Grossinho (403_CR4) 2009; 51
HE Leland (403_CR5) 1985; 40
P Amster (403_CR3) 2005; 303
Y Kabanov (403_CR6) 2009
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– volume: 40
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  article-title: Springer Finance
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– volume: 40
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– volume-title: Markets with Transaction Costs - Mathematical Theory
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– volume-title: Two-Point Boundary Value Problems Lower and Upper Solutions
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– volume: 51
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  publication-title: Int. J. Pure Appl. Math
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– volume-title: Points fixes, points critiques et problèmes aux limites
  year: 1985
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  contributor:
    fullname: J Mawhin
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Snippet We state existence and localisation results for a fully nonlinear boundary value problem using the upper and lower solutions method. With this study we aim to...
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StartPage 146
SubjectTerms Analysis
Approximations and Expansions
Difference and Functional Equations
Jean Mawhin's Achievements in Nonlinear Analysis
Mathematics
Mathematics and Statistics
Ordinary Differential Equations
Partial Differential Equations
Title A fully nonlinear problem arising in financial modelling
URI https://link.springer.com/article/10.1186/1687-2770-2013-146
http://dx.doi.org/10.1186/1687-2770-2013-146
Volume 2013
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