Homogenization and asymptotics for small transaction costs: the multidimensional case

Dylan Possama\"i, H. Mete Soner and Nizar Touzi

Papers from arXiv.org

Abstract: In the context of the multi-dimensional infinite horizon optimal consumption-investment problem with proportional transaction costs, we provide the first order expansion in small transact costs. Similar to the one-dimensional derivation in our accompanying paper [42], the asymptotic expansion is expressed in terms of a singular ergodic control problem, and 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 anymore. Finally, we provide some numerical results which illustrate the structure of the first order optimal controls.

Date: 2012-12, Revised 2013-01
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Citations: View citations in EconPapers (41)

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