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The blow-up technique in terms of stochastics applied to optimal stopping problems in finance
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
(English)Manuscript (Other academic)
Abstract [en]

The blow-up technique is a useful tool for local analysis in PDEtheory. It is applicable to non-linear, higher dimensional PDEs. In this paperwe translate the blow-up technique to stochastic terms by considering thestochastic representation of solutions to PDEs. For illustration we apply theblow-up technique to obtain the early exercise boundary regularity close to expiryfor American put and call options in the classic Black-Scholes framework.

National Category
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-8545OAI: oai:DiVA.org:kth-8545DiVA: diva2:13897
Note
QC 20100629Available from: 2008-05-29 Created: 2008-05-29 Last updated: 2010-06-30Bibliographically 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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http://www.math.kth.se/~teitur/publications/ScalingProbApproach.pdf

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CiteExportLink to record
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Citation style
  • apa
  • harvard1
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More styles
Language
  • de-DE
  • en-GB
  • en-US
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  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
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