Teaching code

4S010697

Teacher

Sara Svaluto-Ferro

Coordinator

Sara Svaluto-Ferro

Credits

6

Language

English

Scientific Disciplinary Sector (SSD)

SECS-S/06 - MATHEMATICAL METHODS OF ECONOMICS, FINANCE AND ACTUARIAL SCIENCES

Period

Semester 2 dal Mar 6, 2023 al Jun 16, 2023.

Lessons timetable Moodle Seminars 0

Learning objectives

The goal of this course is to show the relationship between the main methods of machine learning and the standard methods for financial econometrics. During the course, students will initially be introduced to the fundamentals of Bayesian econometrics (inference, model selection). Then they will be presented with Bayesian Regression and Gaussian Processes (e.g., prices with Gaussian Processes). Subsequently, an in-depth description of supervised learning will be provided (Feedforward neural networks, convexity and inequality constraints, training validation and testing, stochastic gradient descent and neural networks). Interpretability will then be introduced (restrictions on the design of the neural network, power of neural networks, limits to the variance of the Jacobian). In the final part of the course students will have the opportunity to acquire knowledge on the most important modeling concepts of financial econometrics (as a reference for performance). Autoregressive modeling and fitting time series models (Box) and the Jenkins approach will be presented. Finally, the class of probabilistic models for financial data such as hidden Markov, models with Kalman filter, and particle filtering and its application to stochastic volatility models in finance will be introduced. The course ends with the description of advanced neural networks (recurrent neural networks, convolutional neural networks, autoencoders).

Prerequisites and basic notions

For the course, you need to be familiar with programming in Python as well as with basic mathematics.

Program

During the course students will initially be introduced to the fundamentals of Bayesian econometrics (inference, model selection). Then they will be introduced to Bayesian Regression and Gaussian Processes (e.g. pricing and sensitivity with Gaussian Processes). Then they will be given an in-depth description of supervised learning (Feedforward neural networks, convexity and inequality constraints, validation training and testing, stochastic gradient descent). In the second part of the course, students will learn the most important modeling concepts in financial econometrics (as a reference for performance). Autoregressive modeling and calibration of time series models will be presented. This will be followed by the introduction of recurrent neural networks and the comparison of the two approaches and their respective performances. Finally, the Markowitz model for portfolio construction will be introduced and the principle of expected utility optimization explained. After introducing the basics of reinforcement learning, possible applications in this context will be illustrated.

Bibliography

Didactic methods

The course will be divided into theoretical lectures and lessons devoted to explaining and solving theoretical and programming exercises.

Learning assessment procedures

The final grade will be based on a project to be prepared in small groups and a final exam.

Evaluation criteria

To pass the exam, students must demonstrate:
- to have understood the principles underlying the functioning of artificial intelligence methods for financial applications
- to be able to argue in a precise and organic way, without digressions, on artificial intelligence methodologies for finance
- to know how to apply the acquired knowledge to solve application problems presented in the form of exercises, questions and projects.

Criteria for the composition of the final grade

The project and examination contribution to the final grade will be equal.

Exam language

English