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Early exercise boundary regularity close to expiry in the indifference setting: A PDE approach
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
(English)Article in journal (Other academic) Submitted
Abstract [en]

The free boundary problem that occurs when pricing American options is studied in a general setting. We investigate the regularity of the free boundary close to initial state using the so called blow-up technique. This problem has been studied extensively and good results are known for the linear, one-dimensional case. The blow-up technique, however, works also for non-linear PDE in higher dimensions. For illustration we apply the technique to the indierence pricing model where the involved PDE is non-linear.

Keyword [en]
American option, obstacle problem, blow-up, indifference pricing
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-8544OAI: oai:DiVA.org:kth-8544DiVA: diva2:13896
Note
QS 2012Available from: 2008-05-29 Created: 2008-05-29 Last updated: 2012-03-26Bibliographically 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/AmIndRegularity.pdf

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CiteExportLink to record
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Citation style
  • apa
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Output format
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