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摘要翻译：
我们考虑了比例交易费用下的Black-Scholes模型中的长期增长率最大化问题，如Taksar，Klass和Assaf[Math.Oper.Res.13，1988]。与Kallsen和Muhle-Karbe[Ann.appl.probab,20,2010]关于无限视界上的最优消费的研究类似，我们通过确定影子价格来解决这个问题，影子价格是对偶问题的解。它可以显式地计算，直到确定一个确定性函数的根。这反过来又允许显式地计算分数泰勒展开式，无论是对于最优策略的无贸易区域还是对于最优增长率。
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英文标题：
《The dual optimizer for the growth-optimal portfolio under transaction
costs》
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作者：
Stefan Gerhold, Johannes Muhle-Karbe, and Walter Schachermayer
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最新提交年份：
2010
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分类信息：
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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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：Mathematics 数学
二级分类：Probability 概率
分类描述：Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory
概率论与随机过程的理论与应用：例如中心极限定理，大偏差，随机微分方程，统计力学模型，排队论
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英文摘要：
We consider the maximization of the long-term growth rate in the Black-Scholes model under proportional transaction costs as in Taksar, Klass and Assaf [Math. Oper. Res. 13, 1988]. Similarly as in Kallsen and Muhle-Karbe [Ann. Appl. Probab., 20, 2010] for optimal consumption over an infinite horizon, we tackle this problem by determining a shadow price, which is the solution of the dual problem. It can be calculated explicitly up to determining the root of a deterministic function. This in turn allows to explicitly compute fractional Taylor expansions, both for the no-trade region of the optimal strategy and for the optimal growth rate.
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PDF链接：
https://arxiv.org/pdf/1005.5105
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