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Asymptotics for small nonlinear price impact: A PDE approach to the multidimensional case

dc.contributor.authorBayraktar, Erhan
dc.contributor.authorCayé, Thomas
dc.contributor.authorEkren, Ibrahim
dc.date.accessioned2021-02-04T21:53:05Z
dc.date.available2022-02-04 16:53:03en
dc.date.available2021-02-04T21:53:05Z
dc.date.issued2021-01
dc.identifier.citationBayraktar, Erhan; Cayé, Thomas ; Ekren, Ibrahim (2021). "Asymptotics for small nonlinear price impact: A PDE approach to the multidimensional case." Mathematical Finance 31(1): 36-108.
dc.identifier.issn0960-1627
dc.identifier.issn1467-9965
dc.identifier.urihttps://hdl.handle.net/2027.42/166249
dc.description.abstractWe provide an asymptotic expansion of the value function of a multidimensional utility maximization problem from consumption with small nonlinear price impact. In our model, cross‐impacts between assets are allowed. In the limit for small price impact, we determine the asymptotic expansion of the value function around its frictionless version. The leading order correction is characterized by a nonlinear second‐order PDE related to an ergodic control problem and a linear parabolic PDE. We illustrate our result on a multivariate geometric Brownian motion price model.
dc.publisherCambridge University Press
dc.publisherWiley Periodicals, Inc.
dc.subject.otherviscosity solutions
dc.subject.otherhomogenization
dc.subject.othernonlinear price impact portfolio choice
dc.subject.otherasymptotic expansion
dc.titleAsymptotics for small nonlinear price impact: A PDE approach to the multidimensional case
dc.typeArticle
dc.rights.robotsIndexNoFollow
dc.subject.hlbsecondlevelFinance
dc.subject.hlbsecondlevelMathematics
dc.subject.hlbtoplevelBusiness and Economics
dc.subject.hlbtoplevelScience
dc.description.peerreviewedPeer Reviewed
dc.description.bitstreamurlhttp://deepblue.lib.umich.edu/bitstream/2027.42/166249/1/mafi12283_am.pdf
dc.description.bitstreamurlhttp://deepblue.lib.umich.edu/bitstream/2027.42/166249/2/mafi12283.pdf
dc.identifier.doi10.1111/mafi.12283
dc.identifier.doihttps://dx.doi.org/10.7302/172
dc.identifier.sourceMathematical Finance
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dc.working.doi10.7302/172en
dc.owningcollnameInterdisciplinary and Peer-Reviewed


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