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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.|
|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|
|Pages:||2005 - 2046|
|Type of Material:||Journal Article|
|Journal/Proceeding Title:||Communications in Partial Differential Equations|
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