Theory and methods in mathematical and computational finance

该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。在数学和计算金融中，许多理论和应用问题的解决往往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发展，这些方法结合了模型的潜在几何特性，并在应用于非线性数据时反映在性能的提高上。长期目标是开发一种灵活的新元算法，称为非欧几里得升级，将通用近似特性嵌入到各种经典统计技术和机器学习算法中。研究项目还包括为利率、信用风险、波动性的期限结构开发新的随机因素模型，这些模型无套利，能更好地捕捉到观测到的数据的非线性特征。我们也将研究正向倒向随机微分方程的理论、应用和数值解的新方法。该研究项目的预期成果是统计学习，机器学习算法和适用于实际数据的定量金融方面的新方法。加拿大金融部门的效率和竞争力取决于大量多样化的高素质人才的可用性，这些高素质人才接受过定量金融、数据驱动研究、统计理论、机器学习算法和相关行业经验的培训。该研究项目将培养具有创新方法和重要应用的高素质人才，并使他们具备必要的技能进入工业或学术生涯。

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.