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融资中的基本问题，随机建模和统计学习方法。数学和计算融资中许多理论和应用问题的解决方案通常需要创建新的随机建模方法和统计方法。该研究计划考虑了新的统计和机器学习方法的开发，这些方法纳入了模型的基本几何特性，并且在应用于非线性数据时会改善性能。一个长期的目标是开发一种灵活的新元算象，称为非欧国人升级，该升级将通用近似属性嵌入到多种经典的统计技术和机器学习算法中。该研究计划还包括开发新的随机因子模型，以实现利率，信用风险，波动性的术语结构，这些模型无套利，并且更好地捕获了数据的非线性特征。我们还将研究前向后随机微分方程的理论，应用和数值解决方案的新方法。该研究计划的预期结果是适用于真实数据的统计学习，机器学习算法和定量融资的新方法。加拿大金融部门的效率和竞争力取决于通过量化金融，数据驱动研究，统计理论，机器学习算法和相关工业经验的培训的大量高素质人员的可用性。该研究计划将在创新方法和重要应用程序上培训高素质的个人，并允许他们以必要的技能进入工业或学术职业。