MSc Financial Mathematics and Machine Learning

Overview

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.

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Career prospects

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.

Admission requirements for Master’s program

Students must be comfortable with undergraduate-level mathematics: Mathematical analysis, Linear algebra, Probability, and statistics. They also should have Programming experience and acceptable English language qualification. Applicants for the program should have at least a Bachelor’s degree in Mathematics.

Facilities

The Institute of Mathematics, Mechanics and Computer Sciences of Southern Federal University has the material and technical base that provides for all kinds of disciplinary and interdisciplinary training, educational laboratories with modern computers and modern licensed software.

Teaching methods

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.

Basic modules

Mathematics for machine learning. The module is based on supervised learning. Students study theoretical concepts like empirical loss, true loss, cross-validation, regularization, stochastic gradient descent, matrix decompositions 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.

Financial mathematics. The module is focused on the basic problems of financial mathematics related to the computation of option prices and optimal strategies. We mainly consider classical binomial and Black-Scholes models for the evolution of risky assets.

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, we consider Markov processes, martingales, Brownian motion and Ito integral.

Computer technologies. The module includes Python programming and TeX-based publishing systems. It is important to note that the module presents tools for scientific computing and data analysis available via Python libraries.

Applied machine learning and neural networks. The module explains how neutral networks, especially deep neutral networks, are used for solving financial problems.

Insurance mathematics and risk theory. The module studies methods and models suitable for redistribution of risk between parties entering an insurance contract, as well as the theory of optimal portfolios, based on risk, return and utility functions.

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.

Discrete mathematical models. The main objective of the module is to present the basics of mathematical modeling of the complex systems, the methods of their qualitative and quantitative analysis, and the application of the discrete mathematical models to solve real-world problems. In this module students study graph theoretic models of complex systems, pulse processes on directed graphs, the theory of collective choice, Markov chains, and cooperative games.

Stochastic modeling and statistical data processing. The module is focused on Bayesian statistical data models. Its main objective is to teach students to use the complex probabilistic models necessary for data analysis. In addition, students will discuss alternative methods of data analysis.

Levy processes and financial mathematics. Levy processes play an important role in the description of the behavior of risky assets. Students will learn the basics of stochastic analysis based on Levy processes. They will be able to analyze the related problems of 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 will teach students to work with contemporary machine learning and financial literature, adapt general methods to a concrete problem, present the results of the study in the style adopted in the academic literature.

The topic should be 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.