金融资产定价的符号建模

Q1 Mathematics
Xiangwu Zuo, Anxiao (Andrew) Jiang
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引用次数: 0

摘要

符号回归是一种机器学习技术,可以从样本中发现未知函数。与传统的回归技术(如线性回归、多项式回归等)相比,符号回归不会将发现的函数限制为特定的形式(如线性函数、多项式等)。它最近的发展使其应用于各个领域,包括科学研究和工程研究。然而,尽管它的灵活性,符号回归仍然面临一个限制:给定的数据集来自不同的系统在同一领域,符号回归需要找到一个不同的函数为每个数据集,而不是找到一个更一般但简洁的函数,可以通过调整其系数来适应所有的数据集。后一种方法,在本研究中被称为“符号建模”,可以看作是符号回归的推广,在学术界和工业界都有重要的应用。这项工作阐明了符号建模并揭示了一种前沿算法,其原理来自深度学习和遗传编程。该算法被实现到一个应用程序中,展示了其在金融资产定价领域的实际效用,金融资产定价是金融中专注于资产评估的一个重要方面。结果表明,符号模型在多个方面都优于现有的资产定价模型。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Symbolic Modeling for financial asset pricing
Symbolic Regression is a machine learning technique that discovers an unknown function from its samples. Compared to conventional regression techniques (e.g., linear regression, polynomial regression, etc.), Symbolic Regression does not limit the discovered function to specific forms (e.g., linear functions, polynomials, etc.). Its recent developments are enabling its application to various fields, including both scientific study and engineering research. However, in spite of its flexibility, Symbolic Regression still faces one limitation: given datasets from different systems in the same domain, Symbolic Regression needs to find a distinct function for each dataset, instead of finding a more general yet succinct function that can fit all the datasets through the adjustments of its coefficients. The latter approach, which is termed “Symbolic Modeling” in this work, can be seen as a generalization of Symbolic Regression and has important applications to both academia and industry. This work elucidates Symbolic Modeling and unveils a cutting-edge algorithm, deriving its principles from deep learning and genetic programming. This algorithm is implemented into an application, showcasing its practical utility in the field of financial asset pricing, an integral facet of finance that concentrates on asset valuation. It is shown that Symbolic Modeling compares favorably to existing asset pricing models in multiple aspects.
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来源期刊
Journal of Finance and Data Science
Journal of Finance and Data Science Mathematics-Statistics and Probability
CiteScore
3.90
自引率
0.00%
发文量
15
审稿时长
30 days
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