On some nonlinear boundary value problems related to a Black-Scholes model with transaction costs

Thumbnail Image

Files

2015_bound_figueroa_nonlinear.pdf (1.56 MB)
Identifiers
URI: http://hdl.handle.net/10347/21774
ISSN: 1687-2770
DOI: 10.1186/s13661-015-0410-9

Publication date

2015

Authors

Advisors

Tutors

Editors

Journal Title

Journal ISSN

Volume Title

Publisher

Springer
Metrics
Google Scholar
lacobus
Export

Research Projects

Organizational Units

Journal Issue

Abstract

We deal with some generalizations on a Black-Scholes model arising in financial mathematics. As a novelty in this paper, we consider a variable volatility and abstract functional boundary conditions, which allow us to treat a very large class of problems involving Black-Scholes equation. Our main results involve the existence of extremal solutions in presence of lower and upper solutions. Some examples of applications are provided too.

Description

Keywords

Black-Scholes equation| Functional conditions| Discontinuous ODE’s

Bibliographic citation

Figueroa, R., Grossinho, M.d.R. On some nonlinear boundary value problems related to a Black-Scholes model with transaction costs. Bound Value Probl 2015, 145 (2015). https://doi.org/10.1186/s13661-015-0410-9

Relation

Has part

Has version

Is based on

Is part of

Is referenced by

Is version of

Requires

Sponsors

The first author was partially supported by Xunta de Galicia, Consellería de Cultura, Educación e Ordenación Universitaria, through the project EM2014/032 ‘Ecuacións diferenciais non lineares’; and by Ministerio de Economía y Competitividad of Spain under Grant MTM2010-15314, cofinanced by the European Community fund FEDER. The second author was partially funded by Fundação para a Ciência e Tecnologia through the project UID/Multi/00491/2013 and the Transnational Cooperation FCT Portugal-Slovakia ‘Analysis of Nonlinear Partial Differential Equations in Mathematical Finance (2013-2014)’ and by the EU Grant Program FP7-PEOPLE-2012-ITN STRIKE - ‘Novel Methods in Computational Finance’, No. 304617 (D.S.).

Rights

© 2015 Figueroa and Grossinho. This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made

Collections

Estatística, Análise Matemática e Optimización