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arXiv · 1212.6275

Homogenization and asymptotics for small transaction costs: the multidimensional case

Dylan Possamaï·H. Mete Soner·Nizar Touzi
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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.

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Dylan Possamaï, H. Mete Soner, Nizar Touzi. 2013-01-22. Homogenization and asymptotics for small transaction costs: the multidimensional case. https://arxiv.org/abs/1212.6275

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