Probability Theory

Participation Prerequisites

Familiarity with basic calculus and linear algebra is presumed. The text by Sydsæter et al. (2016) provides a good overview.

Course Content

This course covers intermediate and advanced probabilistic concepts indispensable for state-of-art research in finance, economics and data science. In particular, fundamental concepts such as probability, random variables, univariate and multivariate distributions, expectations and limit theorems are reviewed. This is followed by a thorough treatment of such stochastic processes as Markov chains, Brownian motion and martingales. The course finishes by looking at simulations methods. The exposition will follow the treatment in DasGupta (2011).

Intended Learning Outcomes and Competencies

The purpose of this course is to provide doctoral students with the theoretical foun-dations for stochastic modelling in finance, economics and data science. It is intended to prepare participants for frequentist as well as Bayesian approaches to modelling, for classical settings with moderately-sized datasets as well as for modern machine-learning applications with big datasets. By the end of this course, participants will be in a position to understand and interpret state-of-the-art models and to set up such models themselves.

Instruction Type

In-class.

Form of Examination

Each participant will work on a topic of interest and present his or her findings in a presentation in the last lecture.

Literature

DasGupta, A. (2011). Probability for Statistics and Machine Learning. Springer. doi:
10.1007/978-1-4419-9634-3.

Sydsæter, K. et al. (2016). Essential Mathematics for Economic Analysis. 5th edition. Pearson