Sumários

Stochastig integrals

16 Setembro 2024, 12:00 • João Guerra

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

Basic idea of Itô formula as a stochastic chain rule derived from Taylor Theorem. 
Simple example of application of Itô formula. 

Martingales in continuous time. Stochastic integrals of simple processes

10 Setembro 2024, 11:30 • João Guerra

Martingales in continuous time. Definition and Examples. 

Martingales related with Brownian motion. 
Motivation for stochastic integrals. 
Simple processes and stochastic integrals for simple processes. Example. 

Conditional Expectation, Filtrations and martingales

9 Setembro 2024, 12:00 • João Guerra

R code about Geometric Brownian motion simulation. 

Sigma-algebras and filtrations. Examples.
Conditional Expectation main properties. 
Martingale in discrete time. Definition and example. 

Brownian motion and related processes

3 Setembro 2024, 11:30 • João Guerra

Brownian motion properties. 

Brownian motion with drift and geometric Brownian motion: definitions and basic properties. 
Simulation of Brownian motion and geometric Brownian motion with R. 

Presentation of the course. Brownian motion.

2 Setembro 2024, 12:00 • João Guerra

Presentation of the course, programme, bibliography and assessment. 

Introduction to stochastic calculus and its history. 
General concepts about stochastic processes.
Brownian motion: definition.