Sumários

Some concepts of measure and probability and martingales in discrete time

14 Setembro 2026, 12:00 • João Guerra

Some concepts of measure and probability: Sigma-algebras or event spaces, sigma-algebras generated by random variables, examples. Measurable spaces and probability spaces. Filtrations and adapted processes. Example.

Conditional expectation: definition and basic properties.

Martingales in discrete time: definition.

Brownian motion

8 Setembro 2026, 11:30 • João Guerra

Definition of standard Brownian motion and Brownian motion with drift.

Main properties of Brownian motion.

Processes related to Brownian motion: correlated Brownian motion, Geometric Brownian motion. ~

Properties of Geometric Brownian motion.

R scripts examples to simulate Brownian motion and geometric Brownian motion trajectories.

Presentation and introduction to the course and Brownian motion

7 Setembro 2026, 12:00 • João Guerra

Presentation of the course: Syllabus, bibliography, assessment. Introduction to the history of stochastic calculus and mathematical finance. Introduction to Brownian motion.

Definition of stochastic process and examples.

Definition of Brownian motion.