Sumários
Stochastic differential equations
12 Abril 2016, 14:00 • João Guerra
Stochastic differential equations: the Ornstein-Uhlenbeck process with mean reversion.
Financial applications.
The existence and uniqueness of solutions Theorem.
Examples and exercises.
Stochastic differential equations
8 Abril 2016, 14:00 • João Guerra
Stochastic differential equations: motivation and examples.
The geometric Brownian motion. Example.
The Langevin equation and the Ornstein-Uhlenbeck process.
The martingale representation formula
5 Abril 2016, 14:00 • João Guerra
The Itô representation formula. Proof.
Examples.
The martingale representation formula. Proof and examples.
The Itô formula
29 Março 2016, 14:00 • João Guerra
The one-dimensional Itô formula.
Examples and exercises.
The multidimensional Itô formula.
Examples and exercises.
Sketch of the proof of the one-dimensional Itô formula.