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On the size of the non-coincidence set of parabolic obstacle problems with applications to American option pricing
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
2007 (English)In: Mathematica Scandinavica, ISSN 0025-5521, Vol. 101, no 1, 148-160 p.Article in journal (Refereed) Published
Abstract [en]

The following paper is devoted to the study of the positivity set U = {L phi > 0} arising in parabolic obstacle problems. It is shown that U is contained in the non-coincidence set with a positive distance between the boundaries uniformly in the spatial variable if the boundary of U satisfies an interior C-1 -Dini condition in the space variable and a Lipschitz condition in the time variable. We apply our results to American option pricing and we thus show that the positivity set is strictly contained in the continuation region, which means that the option should not be exercised in U or on the boundary of U.

Place, publisher, year, edition, pages
2007. Vol. 101, no 1, 148-160 p.
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-8543ISI: 000250542100009Scopus ID: 2-s2.0-35348952197OAI: oai:DiVA.org:kth-8543DiVA: diva2:13895
Note
QC 20100629Available from: 2008-05-29 Created: 2008-05-29 Last updated: 2010-07-01Bibliographically approved
In thesis
1. PDE methods for free boundary problems in financial mathematics
Open this publication in new window or tab >>PDE methods for free boundary problems in financial mathematics
2008 (English)Doctoral thesis, comprehensive summary (Other scientific)
Abstract [en]

We consider different aspects of free boundary problems that have financial applications. Papers I–III deal with American option pricing, in which case the boundary is called the early exercise boundary and separates the region where to hold the option from the region where to exercise it. In Papers I–II we obtain boundary regularity results by local analysis of the PDEs involved and in Paper III we perform local analysis of the corresponding stochastic representation.

The last paper is different in its character as we are dealing with an optimal switching problem, where a switching of state occurs when the underlying process crosses a free boundary. Here we obtain existence and regularity results of the viscosity solutions to the involved system of variational inequalities.

Place, publisher, year, edition, pages
Stockholm: KTH, 2008. viii, 34 p.
Series
Trita-MAT. MA, ISSN 1401-2278 ; 2008:03
National Category
Mathematics
Identifiers
urn:nbn:se:kth:diva-4777 (URN)978-91-7178-928-0 (ISBN)
Public defence
2008-06-05, Sal F3, KTH, Lindstedtsvägen 26, Stockholm, 14:00
Opponent
Supervisors
Note
QC 20100630Available from: 2008-05-29 Created: 2008-05-29 Last updated: 2010-07-01Bibliographically approved

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