Stochastic Integral

30 Setembro 2015, 08:00 • João Guerra

Stochastic integral: motivation.

Stochastic integral for simple processes. Definition, examples and main properties.

Stochastic integral for adapted processes in the space L^2_{a}. Definition and main properties.

The Itô isometry. Example.

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Martingales

28 Setembro 2015, 10:00 • João Guerra

Conditional expectation.

Main properties.

Martingales in discrete time. Example.

Properties.

Martingales in continuous time.

Properties and examples.

 

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Brownian motion

23 Setembro 2015, 08:00 • João Guerra

Brownian motion and geometrical Brownian motion. Main properties

Examples

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Course overview. Brownian motion

21 Setembro 2015, 10:00 • João Guerra

Course overview. Program, bibliography, assessment.

Introduction and overview: some background and history.

Stochastic processes: general definitions.

Brownian motion: definition and main properties.

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