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A symmetry problem with applications to finance
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
2014 (English)In: Monatshefte für Mathematik (Print), ISSN 0026-9255, E-ISSN 1436-5081, Vol. 174, no 4, 617-626 p.Article in journal (Refereed) Published
Abstract [en]

In this paper we will consider an overdetermined problem in an unknown ring-shaped domain, and we prove that the domain has to be spherical ring. We will apply this problem to an n-dimensional toy model in the mean field game theory introduced by Lasry-Lions too. We show that if in Lasry-Lions model, the additional extra data ”the boundary is a level set” is assumed, then the region, where the solution is harmonic, has to have spherical symmetry.

Place, publisher, year, edition, pages
2014. Vol. 174, no 4, 617-626 p.
Keyword [en]
Mean field game, Symmetry
National Category
URN: urn:nbn:se:kth:diva-134810DOI: 10.1007/s00605-013-0544-8ISI: 000339875900007ScopusID: 2-s2.0-84905013340OAI: diva2:668167

QC 20140901

Available from: 2013-11-29 Created: 2013-11-29 Last updated: 2014-09-01Bibliographically approved
In thesis
1. Essays in Finance Related Problems with PDE Approach
Open this publication in new window or tab >>Essays in Finance Related Problems with PDE Approach
2013 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

This thesis is comprised of three scientific articles, all in PDE problems related to finance. The first two papers address problems concerning bonds and the third one treat s asymmetry problem in the mean field game theory.

We investigate the free boundary for the problem of valuation of American type convertible bond with extra call feature, in paper one. In this case the free boundary behaviour is of interest since it shows the optimal conversion strategy. We study the regularity of the free boundary and also the solution to the pricing of this special financial derivative. The touching point of the free boundary and fixed boundary is discussed, as well.

The second paper is devoted to the study of bonds with call feature and conversion. Further, it is shown that the price of a Bermudan type bond tends to that of an American one on condition that the conversion time goes to the whole life-span of the bond.

Our main goal in the third paper is to investigate a symmetry case regarding the stationary problem in mean field game of Lasry-Lions. Starting with a priori unknown ring-'shaped region, taking the boundaries as level sets and admitting harmonic solutions, it is implied that the region has spherical symmetry. Moreover, therein we attempt to state the model to an higher dimensional case.

Place, publisher, year, edition, pages
Stockholm: KTH Royal Institute of Technology, 2013. vii, 14 p.
Trita-MAT. MA, ISSN 1401-2278 ; 13:04
National Category
Mathematical Analysis
urn:nbn:se:kth:diva-134786 (URN)978-91-7501-959-8 (ISBN)
Public defence
2013-12-16, Sal F3, Lindstedtsvägen 26, KTH, Stockholm, 13:00 (English)

QC 20131129

Available from: 2013-11-29 Created: 2013-11-28 Last updated: 2013-12-12Bibliographically approved

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Sajadini, Sadna
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