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摘要翻译：
在具有比例交易费用的多维无限时域最优消费-投资问题的背景下，给出了小交易费用下的一阶展开式。类似于文献[42]中的一维推导，渐近展开式用奇异遍历控制问题表示，我们的论点是基于粘性解理论和齐次化技术，从而得到一个校正器方程组。与一维情况相比，第一个校正方程的显式解不再可用。最后，我们给出了一些数值结果，说明了一阶最优控制的结构。
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英文标题：
《Homogenization and asymptotics for small transaction costs: the
multidimensional case》
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作者：
Dylan Possama\"i and H. Mete Soner and Nizar Touzi
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最新提交年份：
2013
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分类信息：
一级分类：Mathematics 数学
二级分类：Analysis of PDEs 偏微分方程分析
分类描述：Existence and uniqueness, boundary conditions, linear and non-linear operators, stability, soliton theory, integrable PDE's, conservation laws, qualitative dynamics
存在唯一性，边界条件，线性和非线性算子，稳定性，孤子理论，可积偏微分方程，守恒律，定性动力学
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一级分类：Mathematics 数学
二级分类：Optimization and Control 优化与控制
分类描述：Operations research, linear programming, control theory, systems theory, optimal control, game theory
运筹学，线性规划，控制论，系统论，最优控制，博弈论
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一级分类：Quantitative Finance 数量金融学
二级分类：Portfolio Management 项目组合管理
分类描述：Security selection and optimization, capital allocation, investment strategies and performance measurement
证券选择与优化、资本配置、投资策略与绩效评价
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英文摘要：
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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PDF链接：
https://arxiv.org/pdf/1212.6275
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