Sumários

28 Setembro 2021, 11:30 • João Guerra

Stochastic integrals: motivation.

Stochastic integrals cannot be defined as Riemann integrals.

Simple processes. Definition and examples.

Stochastic integrals for simple processes. Definition, examples and properties.

Stochastic integrals for square-integrable adapted processes. Definition and properties.

Example of computation by definition of a stochastic integral.

24 Setembro 2021, 12:00 • João Guerra

Definition and basic properties of martingales in continuous time. Examples.

Martingales relates with Brownian motion.

Simulation of Brownian motion and geometric Brownian motion using R. Examples.

21 Setembro 2021, 11:30 • João Guerra

Basic properties of Brownian motion. Correlated Brownian motion and Geometric Brownian motion.

Discussion of an exercise about Brownian motion.

Conditional Expectation. Definition and basic properties.

Filtrations and martingales in Discrete time. Example.

17 Setembro 2021, 12:00 • João Guerra

Brownian motion: definition and basic properties.

Brownian motion with drift: definition and properties.

Approximation of Brownian motion by a sequence of simple random walks.

14 Setembro 2021, 11:30 • João Guerra

Presentation of the course: Programme, Bibliography and assessment.