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Affine Volterra processes

hal.structure.identifierCEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
dc.contributor.authorAbi Jaber, Eduardo
hal.structure.identifierDepartment of Mathematics - ETH
dc.contributor.authorLarsson, Martin
hal.structure.identifierLaboratoire de Mathématiques et Modélisation d'Evry [LaMME]
dc.contributor.authorPulido, Sergio
dc.date.accessioned2019-12-20T10:55:07Z
dc.date.available2019-12-20T10:55:07Z
dc.date.issued2019
dc.identifier.issn1050-5164
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/20361
dc.language.isoenen
dc.subjectstochastic Volterra equationsen
dc.subjectRiccati-Volterra equationsen
dc.subjectrough volatilityen
dc.subjectaffine processesen
dc.subject.ddc519en
dc.titleAffine Volterra processesen
dc.typeArticle accepté pour publication ou publié
dc.description.abstractenWe introduce affine Volterra processes, defined as solutions of certain stochastic convolution equations with affine coefficients. Classical affine diffusions constitute a special case, but affine Volterra processes are neither semimartingales, nor Markov processes in general. We provide explicit exponential-affine representations of the Fourier–Laplace functional in terms of the solution of an associated system of deterministic integral equations of convolution type, extending well-known formulas for classical affine diffusions. For specific state spaces, we prove existence, uniqueness, and invariance properties of solutions of the corresponding stochastic convolution equations. Our arguments avoid infinite-dimensional stochastic analysis as well as stochastic integration with respect to non-semimartingales, relying instead on tools from the theory of finite-dimensional deterministic convolution equations. Our findings generalize and clarify recent results in the literature on rough volatility models in finance.en
dc.relation.isversionofjnlnameThe Annals of Applied Probability
dc.relation.isversionofjnlvol29en
dc.relation.isversionofjnlissue5en
dc.relation.isversionofjnldate2019-10
dc.relation.isversionofjnlpages3155-3200en
dc.relation.isversionofdoi10.1214/19-AAP1477en
dc.relation.isversionofjnlpublisherInstitute of Mathematical Statisticsen
dc.subject.ddclabelProbabilités et mathématiques appliquéesen
dc.relation.forthcomingnonen
dc.relation.forthcomingprintnonen
dc.description.ssrncandidatenonen
dc.description.halcandidatenonen
dc.description.readershiprechercheen
dc.description.audienceInternationalen
dc.relation.Isversionofjnlpeerreviewedouien
dc.relation.Isversionofjnlpeerreviewedouien
dc.date.updated2019-12-20T10:52:42Z
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