英文标题：
《Asymptotic approximation of optimal portfolio for small time horizons》
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作者：
Rohini Kumar and Hussein Nasralah
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最新提交年份：
2018
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英文摘要：
We consider the problem of portfolio optimization in a simple incomplete market and under a general utility function. By working with the associated Hamilton-Jacobi-Bellman partial differential equation (HJB PDE), we obtain a closed-form formula for a trading strategy which approximates the optimal trading strategy when the time horizon is small. This strategy is generated by a first order approximation to the value function. The approximate value function is obtained by constructing classical sub- and super-solutions to the HJB PDE using a formal expansion in powers of horizon time. Martingale inequalities are used to sandwich the true value function between the constructed sub- and super-solutions. A rigorous proof of the accuracy of the approximation formulas is given. We end with a heuristic scheme for extending our small-time approximating formulas to approximating formulas in a finite time horizon.
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中文摘要：
我们考虑了一个简单不完全市场和一般效用函数下的投资组合优化问题。通过使用相关的Hamilton-Jacobi-Bellman偏微分方程（HJB-PDE），我们得到了一个交易策略的封闭式公式，该公式在时间范围很小时近似于最优交易策略。该策略由值函数的一阶近似值生成。通过构造HJB PDE的经典子解和超解，利用水平时间幂的形式化展开，得到近似值函数。鞅不等式用于在构造的子解和超解之间夹心真值函数。对近似公式的精度给出了严格的证明。最后，我们给出了一个启发式方案，将我们的小时间近似公式扩展到有限时间范围内的近似公式。
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分类信息：

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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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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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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