Itô's formula

30 Setembro 2013, 10:00 • João Guerra

Itô's formula. One-dimensional case and multidimensional formula. Examples, exercises and basic ideas of the proof.

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Stochastic integrals

24 Setembro 2013, 09:30 • João Guerra

Itô stochastic integrals of simple processes. Examples and properties.

Itô stochastic integrals of adapted processes. Examples and properties.

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Martingales and introduction to stochastic calculus

23 Setembro 2013, 10:00 • João Guerra

Martingales in continuous time. Examples and exercises.

Stochastic integrals and stochastic calculus: motivation and introduction.

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Geometrical Brownian motion. Martingales.

17 Setembro 2013, 09:30 • João Guerra

Brownian motion and geometrical Brownian motion.

Conditional Expectation.

The concept of filtration in a probability space.

Martingales in discrete time. Main properties.

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Course Overview. Brownian motion.

16 Setembro 2013, 10:00 • João Guerra

Course overview. Programme, bibliography, assessment.

Introduction and overview: some background and history.

Stochastic processes: general definitions.

Brownian motion: definition and main properties.

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