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A PDE approach to regularity of solutions to finite horizon optimal switching problems
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).ORCID iD: 0000-0002-6608-0715
Yerevan State Univ, Dept Math & Mech.
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).ORCID iD: 0000-0002-1316-7913
2009 (English)In: Nonlinear Analysis, ISSN 0362-546X, E-ISSN 1873-5215, Vol. 71, no 12, 6054-6067 p.Article in journal (Refereed) Published
Abstract [en]

We study optimal 2-switching and n-switching problems and the corresponding system of variational inequalities. We obtain results on the existence of viscosity solutions for the 2-switching problem for various setups when the cost of switching is non-deterministic. For the n-switching problem we obtain regularity results for the solutions of the variational inequalities. The solutions are C-l,C-l-regular away for the free boundaries of the action sets.

Place, publisher, year, edition, pages
2009. Vol. 71, no 12, 6054-6067 p.
Keyword [en]
Real options; Security design; Backward stochastic differential equation; Default risk; Snell envelope; Stopping time; Stopping and starting; Optimal switching; Viscosity solution of PDEs; Variational inequalities; INVESTMENTS
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-8546DOI: 10.1016/j.na.2009.05.063ISI: 000272606300015Scopus ID: 2-s2.0-72149106819OAI: oai:DiVA.org:kth-8546DiVA: diva2:13898
Note
QC 20100630Available 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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Djehiche, BoualemShahgholian, Henrik

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