Homogenization and Asymptotics for Small Transaction Costs: The Multidimensional Case
Possamaï, Dylan; Soner, Halil Mete; Touzi, Nizar (2015), Homogenization and Asymptotics for Small Transaction Costs: The Multidimensional Case, Communications in Partial Differential Equations, 40, 11, p. 2005-2046. 10.1080/03605302.2015.1053916
TypeArticle accepté pour publication ou publié
External document linkhttps://arxiv.org/abs/1212.6275v2
Journal nameCommunications in Partial Differential Equations
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Abstract (EN)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.
Subjects / KeywordsAsymptotic expansions; Homogenization; Transaction costs; Viscosity solutions
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