英文标题：
《A multi-asset investment and consumption problem with 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 study a multi-asset version of the Merton investment and consumption problem with proportional transaction costs. In general it is difficult to make analytical progress towards a solution in such problems, but we specialise to a case where transaction costs are zero except for sales and purchases of a single asset which we call the illiquid asset. Assuming agents have CRRA utilities and asset prices follow exponential Brownian motions we show that the underlying HJB equation can be transformed into a boundary value problem for a first order differential equation. The optimal strategy is to trade the illiquid asset only when the fraction of the total portfolio value invested in this asset falls outside a fixed interval. Important properties of the multi-asset problem (including when the problem is well-posed, ill-posed, or well-posed only for large transaction costs) can be inferred from the behaviours of a quadratic function of a single variable and another algebraic function.
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中文摘要：
在本文中，我们研究了具有比例交易成本的默顿投资和消费问题的多资产版本。一般来说，很难在这些问题的解决方案方面取得分析性进展，但我们专门研究交易成本为零的情况，除非出售和购买单一资产，我们称之为非流动资产。假设代理具有CRRA效用，资产价格遵循指数布朗运动，我们表明，基本HJB方程可以转化为一阶微分方程的边值问题。最佳策略是，只有当投资于该资产的总投资组合价值的一部分超出固定区间时，才交易非流动资产。多资产问题的重要性质（包括当问题是适定的、不适定的或仅针对大交易成本的适定的）可以从单个变量的二次函数和另一个代数函数的行为推断出来。
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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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