Machine learning penetrates various spheres of human activity. Its role will only grow in the foreseeable future. In the educational market, there are various training programs for specialists in the field of data analysis and machine learning as well as economic and mathematical training programs. However, the combination of the financial mathematics methods and machine learning technologies is unique and promising. Specialists with such knowledge will be in demand in various organizations operating in the financial market.
The program is designed to train students in both practical and theoretical aspects of machine learning. The potential applications will be focused on quantitative finance. The program combines IT, mathematics, and finance. Its aim is to introduce students to the modern problems of machine learning and financial mathematics as well as to present methods, suitable for dealing with these problems.
The graduates of the Master's program will be prepared for independent work in finance, banking, insurance, retail, e-commerce. Typical employment opportunities are data science departments of banks, financial and consulting companies.
Master’s graduation work may be a good starting point for Ph.D. studies. After obtaining an MSc, it is possible to continue studies and apply for admission to a four-year Ph.D. program.
The program consists of a combination of lectures, practical sessions, project work, and seminar discussions. Student performance is assessed through examinations, coursework, and projects. Modern methods of data analysis and decision making require tools from probability, statistics, optimization, machine learning, scientific calculations. The program will present these tools in an accessible way through numerous examples. The students will learn machine learning software and get the experience of using it for the analysis of financial problems. Supervised independent work of students includes elements of research work in the field of mathematical modeling and data analysis.
Selected topics in probability and statistics. The module contains information, which is necessary for the understanding of the financial market models and the mathematical foundations of machine learning. Along with standard topics in probability and statistics like expectation, variance, correlation, conditional expectation, Bayes formulas, parameter estimation, and hypothesis testing, it considers the basics of martingales and Markov processes.
Machine learning: the mathematical basis. The module includes the basics of statistical learning theory, convex optimization methods and their applications to machine learning problems, the basics of online learning theory and its applications to optimal investment problems.
Financial mathematics. The module is focused on the basic problems of financial mathematics related to the computation of option prices and optimal strategies. Discrete-time models, as well as continuous-time models based on Brownian motion and Levy processes, are considered.
Computer technologies. The module gives basic knowledge about the principles of constructing and implementing the algorithms for solving mathematical modeling problems, methods for parallelizing algorithms, numerical methods for solving the systems of algebraic and differential equations, results on the properties of initial-boundary value problems, computational experiment, and visualization of scientific research results.
Applied machine learning and neural networks. The module is devoted to the study of modern methods and technologies of machine learning. Students will study theoretical concepts like empirical loss, cross-validation, regularization, as well as concrete models: Linear regression, Logistic regression, Nearest neighbors, Support vector machines, Random forest, Neural networks. An important part of the course is the implementation of basic algorithms via Python libraries.
Econometrics. The module discusses the classical econometric fields: linear models, non-linear ARCH and stochastic volatility models, long-memory models, as well as the methods of multidimensional applied statistics: factor analysis, discriminant, and cluster analysis. After this module, the students will be able to evaluate the parameters and implement the econometric models.
Levy processes and financial mathematics. The module studies the modern methods and technologies of Levy processes. In particular, this includes the study of the theory of Levy processes as the basic models of financial time series, acquaintance with the basic methods of stochastic analysis with Levy processes, calculation of the functionals of Levy processes, applications of Levy processes in financial mathematics.
Game theory and its applications. The main objective of the module is to teach the basics of mathematical modeling of conflicts and cooperation in social and economic systems by the means of the game theory. The module includes static and dynamic games with complete and incomplete information.
The research seminar and Master’s thesis
The Research seminar teaches students to work with contemporary machine learning and financial literature, to adapt general methods to a concrete problem, and to present the results of the study in the style adopted in the academic literature. The topics are related to the analysis of derivative securities, optimal portfolios, and prediction of financial indexes. It is assumed that most projects will involve the methods of machine learning.