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Homogenization and Asymptotics for Small Transaction Costs: The Multidimensional Case

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

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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.
Publication Date: 1-Jan-2015
Citation: Possamaï, 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:10.1080/03605302.2015.1053916
DOI: doi:10.1080/03605302.2015.1053916
ISSN: 0360-5302
EISSN: 1532-4133
Pages: 2005 - 2046
Type of Material: Journal Article
Journal/Proceeding Title: Communications in Partial Differential Equations
Version: Author's manuscript

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