Theory and methods in mathematical and computational finance

数学和计算金融的理论和方法

• 批准号: RGPIN-2021-04112
• 负责人: Hyndman, Cody
• 金额: $ 1.53万
• 依托单位: Concordia University
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2022
• 资助国家: 加拿大
• 起止时间: 2022-01-01 至 2023-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=759001
• 关键词: Theory; methods; mathematical; computational; finance

The focus of the proposed research program is on fundamental problems, stochastic modelling, and statistical learning methods in mathematical and computational finance. The solution of many theoretical and applied problems in mathematical and computational finance often requires the creation of new stochastic modelling approaches and statistical methodology. The research program considers the development of new statistical and machine learning methods that incorporate underlying geometric properties of models and that are reflected in improved performance when applied to nonlinear data.  A long-term objective is to develop of a flexible new meta-algorithm, called non-Euclidean upgrading, that embeds universal approximation properties into a wide variety of classical statistical techniques and machine learning algorithms. The research program also includes the development of new stochastic factor models for the term-structure of interest rates, credit-risk, volatility that are arbitrage-free and better capture the observed nonlinear features of the data. We shall also investigate new approaches to the theory, applications, and numerical solution of forward-backward stochastic differential equations. The expected outcomes of this program of research are novel methods in statistical learning, machine learning algorithms, and quantitative finance that are applicable to real data.  The efficiency and competitiveness of the Canadian financial sector depends on the availability of a large and diverse pool of highly qualified personnel with training in quantitative finance, data-driven research, statistical theory, machine learning algorithms, and relevant industrial experience. The research program will train highly qualified personal on innovative methods and important applications and allow them to enter industrial or academic careers with the necessary skills.

拟议的研究计划的重点是数学和计算金融中的基本问题、随机建模和统计学习方法。要解决数学和计算金融中的许多理论和应用问题，往往需要创造新的随机建模方法和统计方法。该研究计划考虑开发新的统计和机器学习方法，这些方法结合了模型的基本几何属性，并在应用于非线性数据时的性能改善中得到反映。长期目标是开发一种灵活的新元算法，称为非欧几里德升级，将普遍逼近属性嵌入到各种经典统计技术和机器学习算法中。研究计划还包括开发新的随机因素模型，用于利率、信用风险、波动率的期限结构，这些模型是无套利的，并更好地捕获数据的观察到的非线性特征。我们还将研究向前-向后随机微分方程的理论、应用和数值解的新方法。这项研究计划的预期成果是适用于真实数据的统计学习、机器学习算法和量化金融方面的新方法。加拿大金融部门的效率和竞争力取决于是否有大量和多样化的高素质人才，他们接受过量化金融、数据驱动研究、统计理论、机器学习算法和相关行业经验方面的培训。该研究计划将在创新方法和重要应用方面培训高素质的个人，并允许他们以必要的技能进入工业或学术职业生涯。