英文标题：
《Optimal consumption and investment under transaction costs》
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作者：
David Hobson, Alex S.L. Tse, Yeqi Zhu
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最新提交年份：
2016
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英文摘要：
In this article we consider the Merton problem in a market with a single risky asset and transaction costs. We give a complete solution of the problem up to the solution of a free-boundary problem for a first-order differential equation, and find that the form of the solution (whether the problem is well-posed, whether the problem is well-posed only for large transaction costs, whether the no-transaction wedge lies in the first, second or fourth quadrants) depends only on a quadratic whose co-efficients are functions of the parameters of the problem, and then only through the value and slope of this quadratic at zero, one and the turning point. We find that for some parameter values and for large transaction costs the location of the boundary at which sales of the risky asset occur is independent of the transaction cost on purchases. We give both a mathematical and financial reason for this phenomena.
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中文摘要：
在本文中，我们考虑了具有单一风险资产和交易成本的市场中的默顿问题。我们给出了问题的完整解，直到一阶微分方程的自由边界问题的解，并发现解的形式（问题是否适定，问题是否仅针对大交易成本适定，无交易楔子是否位于第一、第二或第四象限）仅取决于系数为问题参数函数的二次型，然后仅通过该二次型的值和斜率为零，一是转折点。我们发现，对于某些参数值和大交易成本，风险资产出售的边界位置与购买的交易成本无关。我们给出了这种现象的数学和财务原因。
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分类信息：

一级分类：Quantitative Finance 数量金融学
二级分类：Mathematical Finance 数学金融学
分类描述：Mathematical and analytical methods of finance, including stochastic, probabilistic and functional analysis, algebraic, geometric and other methods
金融的数学和分析方法，包括随机、概率和泛函分析、代数、几何和其他方法
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