Show simple item record

AuthorEinemann, Michaeldc.contributor.author
Date of accession2016-03-14T15:20:08Zdc.date.accessioned
Available in OPARU since2016-03-14T15:20:08Zdc.date.available
Year of creation2008dc.date.created
AbstractThe aim of this thesis is to highlight the role of semigroup theory in mathematical finance and to provide a class of useful methods. Apart from this special task, several new results concerning invariant subsets of strongly continuous semigroups and regular perturbations of sesquilinear forms (related to the classical Kato class) are given. A major step in finance was the pioneering work of Black and Scholes. They showed that prices of financial derivatives can be obtained as solutions of partial differential equations. Solving this equation "by hand", they derived the famous Black-Scholes formula which is still in use today. But with those partial differential equations we are deep in the theory of strongly continuous semigroups. In fact, rewriting the equations in terms of a differential operator one can interpret this as a Cauchy problem. If the operator now generates a strongly continuous semigroup, then the solution of the Cauchy problem and thus the price of the derivative is obtained from the semigroup. Therefore, it is of great interest to determine whether the Black-Scholes operator (or other differential operators arising in mathematical finance) generates a strongly continuous semigroup or not. The idea of Black and Scholes also shows a change of drift in the price process, which can be interpreted as a perturbation of the associated differential operator. In taking a kind of reverse point of view and studying the structure of price operators in an arbitrage-free market it is further shown that these form an evolution family of linear, positive, injective operators. Moreover, some order intervals are invariant under this family. We take these statements as a motivation inspiring the following four main topics of the thesis: invariant subsets of strongly continuous semigroups, semigroups of injective operators, perturbation results for differential operators, generation results for the Black-Scholes operator.dc.description.abstract
Languageendc.language.iso
PublisherUniversität Ulmdc.publisher
LicenseStandard (Fassung vom 01.10.2008)dc.rights
Link to license texthttps://oparu.uni-ulm.de/xmlui/license_v2dc.rights.uri
Dewey Decimal GroupDDC 510 / Mathematicsdc.subject.ddc
LCSHDifferential operatorsdc.subject.lcsh
LCSHFinance. Mathematical methodsdc.subject.lcsh
LCSHSemigroups of operatorsdc.subject.lcsh
TitleSemigroup methods in financedc.title
Resource typeDissertationdc.type
DOIhttp://dx.doi.org/10.18725/OPARU-1086dc.identifier.doi
PPN590374966dc.identifier.ppn
URNhttp://nbn-resolving.de/urn:nbn:de:bsz:289-vts-66668dc.identifier.urn
GNDBlack-Scholes-Modelldc.subject.gnd
GNDFinanzmathematikdc.subject.gnd
GNDOperatorfamiliedc.subject.gnd
FacultyFakultät für Mathematik und Wirtschaftswissenschaftenuulm.affiliationGeneral
Date of activation2009-01-16T10:59:53Zuulm.freischaltungVTS
Peer reviewneinuulm.peerReview
Shelfmark print versionZ: J-H 13.249; N: J-H 9.858uulm.shelfmark
DCMI TypeTextuulm.typeDCMI
VTS-ID6666uulm.vtsID
CategoryPublikationenuulm.category


Files in this item

Thumbnail

This item appears in the following Collection(s)

Show simple item record