Publication:
Exact solvability of stochastic differential equations driven by finite activity levy processes

dc.contributor.coauthorÜnal G.
dc.contributor.departmentDepartment of Mathematics
dc.contributor.departmentGraduate School of Sciences and Engineering
dc.contributor.kuauthorÇağlar, Mine
dc.contributor.kuauthorİyigünler, İsmail
dc.contributor.schoolcollegeinstituteCollege of Sciences
dc.contributor.schoolcollegeinstituteGRADUATE SCHOOL OF SCIENCES AND ENGINEERING
dc.date.accessioned2024-11-09T13:26:18Z
dc.date.issued2012
dc.description.abstractWe consider linearizing transformations of the one-dimensional nonlinear stochastic differential equations driven by Wiener and compound Poisson processes, namely finite activity Levy processes. We present linearizability criteria and derive the required transformations. We use a stochastic integrating factor method to solve the linearized equations and provide closed-form solutions. We apply our method to a number ofstochastic differential equations including Cox-Ingersoll-Ross short-term interest rate model, log-mean reverting asset pricing model and geometric Ornstein- Uhlenbeck equation all with additional jump terms. We use their analytical solutions to illustrate the accuracy of the numerical approximations obtained from Euler and Maghsoodi discretization schemes. The means of the solutions are estimated through Monte Carlo method.
dc.description.fulltextYES
dc.description.indexedbyScopus
dc.description.openaccessYES
dc.description.publisherscopeInternational
dc.description.sponsoredbyTubitakEuN/A
dc.description.sponsorshipN/A
dc.description.versionPublisher version
dc.identifier.eissn2297-8747
dc.identifier.embargoNO
dc.identifier.filenameinventorynoIR00520
dc.identifier.issn1300-686X
dc.identifier.quartileN/A
dc.identifier.scopus2-s2.0-84859377032
dc.identifier.urihttps://hdl.handle.net/20.500.14288/3479
dc.keywordsAnalytical solutions
dc.keywordsAsset pricing model
dc.keywordsClosed form solutions
dc.keywordsCompound poisson process
dc.keywordsDiscretization scheme
dc.keywordsIntegrating factor
dc.keywordsIntegrating factor methods
dc.keywordsInterest rate models
dc.keywordsLevy process
dc.keywordsLinearizability
dc.keywordsLinearized equations
dc.keywordsNumerical approximations
dc.keywordsStochastic differential equations
dc.keywordsLinearization
dc.keywordsMonte Carlo methods
dc.keywordsPoisson distribution
dc.keywordsRandom processes
dc.keywordsStochastic systems
dc.keywordsDifferential equations
dc.keywordsLevy processes
dc.keywordsLinearization
dc.keywordsStochastic differential equations
dc.keywordsStochastic integrating factors
dc.language.isoeng
dc.publisherMultidisciplinary Digital Publishing Institute (MDPI)
dc.relation.ispartofMathematical and Computational Applications
dc.relation.urihttp://cdm21054.contentdm.oclc.org/cdm/ref/collection/IR/id/588
dc.subjectMathematics
dc.titleExact solvability of stochastic differential equations driven by finite activity levy processes
dc.typeJournal Article
dspace.entity.typePublication
local.contributor.kuauthorİyigünler, İsmail
local.contributor.kuauthorÇağlar, Mine
local.publication.orgunit1GRADUATE SCHOOL OF SCIENCES AND ENGINEERING
local.publication.orgunit1College of Sciences
local.publication.orgunit2Department of Mathematics
local.publication.orgunit2Graduate School of Sciences and Engineering
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