英文标题：
《Semiclassical approximation in stochastic optimal control I. Portfolio
construction problem》
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作者：
Sakda Chaiworawitkul, Patrick S. Hagan, and Andrew Lesniewski
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最新提交年份：
2014
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英文摘要：
This is the first in a series of papers in which we study an efficient approximation scheme for solving the Hamilton-Jacobi-Bellman equation for multi-dimensional problems in stochastic control theory. The method is a combination of a WKB style asymptotic expansion of the value function, which reduces the second order HJB partial differential equation to a hierarchy of first order PDEs, followed by a numerical algorithm to solve the first few of the resulting first order PDEs. This method is applicable to stochastic systems with a relatively large number of degrees of freedom, and does not seem to suffer from the curse of dimensionality. Computer code implementation of the method using modest computational resources runs essentially in real time. We apply the method to solve a general portfolio construction problem.
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中文摘要：
这是我们研究求解随机控制理论中多维问题的Hamilton-Jacobi-Bellman方程的有效近似格式的一系列论文中的第一篇。该方法结合了价值函数的WKB式渐近展开，将二阶HJB偏微分方程简化为一阶偏微分方程，然后用数值算法求解得到的前几个一阶偏微分方程。这种方法适用于自由度相对较大的随机系统，并且似乎不受维数灾难的影响。使用少量计算资源实现该方法的计算机代码基本上是实时运行的。我们应用该方法来解决一个一般的投资组合构建问题。
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分类信息：

一级分类：Quantitative Finance 数量金融学
二级分类：Computational Finance 计算金融学
分类描述：Computational methods, including Monte Carlo, PDE, lattice and other numerical methods with applications to financial modeling
计算方法，包括蒙特卡罗，偏微分方程，格子和其他数值方法，并应用于金融建模
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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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