Machine Learning for Continuous-Time Economics
Machine Learning for Continuous-Time Economics
复制标题
连续时间经济学的机器学习
DOI：
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发表时间：
2018
期刊：
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通讯作者：
V. Duarte
中科院分区：
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作者：
V. Duarte
提出了一种求解金融经济中一大类非线性连续时间模型的全局算法。利用机器学习的工具，将求解相应的非线性偏微分方程组的问题转化为一系列有监督的学习问题。为了说明该方法的适用范围，我对非平凡基准模型进行了求解，并将数值解与解析解进行了比较。此外，我还提出了一个测试和评估解决方案方法的环境。在新古典增长模型的背景下，给定任意值函数，生产率函数被逆工程处理，使得与最优化问题对应的哈密尔顿-雅可比-贝尔曼方程恒为零。这为解决方法提供了一个试验场，并提供了比较它们的客观方式。结果表明，该方法具有较高的精度，可以处理高达10维的非线性模型。最后，我提供了一个实现该算法的开源库。
This paper proposes a global algorithm to solve a large class of nonlinear continuous-time models in finance and economics. Using tools from machine learning, I recast problem of solving the corresponding nonlinear partial differential equations as a sequence of supervised learning problems. To illustrate the scope of the method, I solve nontrivial benchmark models and compare the numerical solution with the analytical ones. Furthermore, I propose a setting to test and evaluate solution methods. In the context of a neoclassical growth model, given any value function, the productivity function is reverse engineered so that the Hamilton-Jacobi-Bellman equation corresponding to the optimization problem is identically zero. This provides a testing ground for solution methods and an objective way of comparing them. Results indicate that the method is accurate and can handle nonlinear models with as many as 10 dimensions. Finally, I provide an open source library that implements the proposed algorithm.