# Homogenization and Asymptotics for Small Transaction Costs: The Multidimensional Case

## Author(s): Possamaï, D; Soner, H Mete; Touzi, N

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DC FieldValueLanguage
dc.contributor.authorPossamaï, D-
dc.contributor.authorSoner, H Mete-
dc.contributor.authorTouzi, N-
dc.date.accessioned2021-10-11T14:18:05Z-
dc.date.available2021-10-11T14:18:05Z-
dc.date.issued2015-01-01en_US
dc.identifier.citationPossamaï, D, Soner, HM, Touzi, N. (2015). Homogenization and Asymptotics for Small Transaction Costs: The Multidimensional Case. Communications in Partial Differential Equations, 40 (11), 2005 - 2046. doi:10.1080/03605302.2015.1053916en_US
dc.identifier.issn0360-5302-
dc.identifier.urihttp://arks.princeton.edu/ark:/88435/pr1qk3n-
dc.description.abstract© 2015, Taylor & Francis Group, LLC. In the context of the multi-dimensional infinite horizon optimal consumption investment problem with small proportional transaction costs, we prove an asymptotic expansion. Similar to the one-dimensional derivation in our accompanying paper, the first order term is expressed in terms of a singular ergodic control problem. Our arguments are based on the theory of viscosity solutions and the techniques of homogenization which leads to a system of corrector equations. In contrast with the one-dimensional case, no explicit solution of the first corrector equation is available and we also prove the existence of a corrector and its properties. Finally, we provide some numerical results which illustrate the structure of the first order optimal controls.en_US
dc.format.extent2005 - 2046en_US
dc.language.isoen_USen_US
dc.relation.ispartofCommunications in Partial Differential Equationsen_US
dc.rightsAuthor's manuscripten_US
dc.titleHomogenization and Asymptotics for Small Transaction Costs: The Multidimensional Caseen_US
dc.typeJournal Articleen_US
dc.identifier.doidoi:10.1080/03605302.2015.1053916-
dc.identifier.eissn1532-4133-
pu.type.symplectichttp://www.symplectic.co.uk/publications/atom-terms/1.0/journal-articleen_US

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