Theory and methods in mathematical and computational finance

点击翻译按钮获取中文摘要

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.