Sumários
26 Setembro 2023, 11:30
•
João Guerra
Exercise on martingales in continuous time.
Stochastic integral of adapted processes. Definition and properties.
Itô formula. Motivation.
Definition of Itô process.
Itô formula in the one-dimensional case. Examples.
22 Setembro 2023, 10:00
•
João Guerra
Martingales in continuous time. Examples.
Exercises on Brownian motion.
Motivation for the definition of stochastic integral.
Definition of simple process.
Stochastic integral of simple processes. Properties of stochastic integral of simple processes. Examples.
19 Setembro 2023, 11:30
•
João Guerra
Simulation of Brownian motion and Geometric Brownian motion trajectories with R and the packahe SDE.
Conditional Expectation - Definition and properties.
Martingales in discrete time: definition and properties.
Examples.
15 Setembro 2023, 10:00
•
João Guerra
Brownian motion definition and main properties.
Brownian motion with drift.
Correlated Brownian motion.
Geometric Brownian motion. Definition and properties.
12 Setembro 2023, 11:30
•
João Guerra
Presentation of the course, bibliography, assessment method.
Brief introduction to the history of Brownian motion and stochastic calculus.
Stochastic processes. Examples.
Brownian motion. Definition and convergence of random walks to Brownian motion.