Sumários
4 Outubro 2022, 11:30
•
João Guerra
Deterministic differential equations: examples.
Stochastic Differential Equations: definitions and examples.
Existence and uniqueness of solutions. Example of explosion of a solution in finite time.
The geometric Brownian motion SDE. Two different methods for obtaining the solution.
How to solve the Langevin or Ornstein-Uhlenbeck SDE.
29 Setembro 2022, 11:30
•
João Guerra
Itô Formula: motivation.
Itô processes: definition.
One-dimensional Itô formula: different versions and examples.
Multidimensional Itô formula.
27 Setembro 2022, 11:30
•
João Guerra
Simple processes. Definition and example.
Stochastic integral of simple processes. Definition and properties. Example.
Stochastic integral of adapted processes. Definition and properties. Example.
23 Setembro 2022, 12:00
•
João Guerra
Martingales in Discrete time and in continuous time.
Definition, properties and examples.
20 Setembro 2022, 11:30
•
João Guerra
Correlated Brownian motion.
Geometric Brownian motion: definition,
Properties and simulation of trajectories using R
and the package SDE.
Conditional expectation: definition and properties.
Filtration and martingale in discrete time: definition,
properties and examples.