Existence and uniqueness of solutions for SDE's

5 Abril 2017, 09:00 • João Guerra

Existence and uniqueness of solutions Theorem for SDE's. Examples.

The Ornstein-Uhlenbeck process with mean reversion and a financial
application: the Vasicek model for interest rates.

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Stochastic Differential Equations

31 Março 2017, 09:00 • João Guerra

Exercises on the application of Itô formula. 

Stochastic Differential Equations: Motivation and examples. Some examples: stochastic differential equation for the geometric Brownian motion and the Langevin equation for the Ornstein-Uhlenbeck process.

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Ito representation theorem and martingale representation theorem,

29 Março 2017, 09:00 • João Guerra

Itô representation theorem and martingale representation theorem. 

Examples and exercises. 

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Exercises and multidimensional Ito formula

24 Março 2017, 09:00 • João Guerra

Exercises on the application of Ito formula. 

Multidimensional Ito processes and multidimensional Ito formula. 

Examples and exercises. 

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Itô formula

22 Março 2017, 09:00 • João Guerra

The stochastic integral for processes u in the class L_{a,T}.

Itô processes: definition.

Itô formula or Itô Lemma for functions of one-dimensional Itô processes and functions of the Brownian motion. Examples and sketch of the proof.

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