Stochastic integrals

1 Outubro 2014, 08:00 • João Guerra

Stochastic differential equations and stochastic integrals: introduction and motivation.

Riemann-Stieltjes integral and why the stochastic integral cannot be defined in this way.

Itô stochastic integrals of simple processes. Examples and properties.

Itô stochastic integrals of adapted processes. Examples and properties.

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Martingales. Examples and exercises.

29 Setembro 2014, 10:00 • João Guerra

Martingales in descrete and continuous time.

Examples and exercises.

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Brownian motion. Geometrical Brownian motion. Conditional expectation. Filtrations and martingales

24 Setembro 2014, 08:00 • João Guerra

Brownian motion and geometrical Brownian motion. Main properties

Conditional Expectation.

The concept of filtration in a probability space.

Martingales in discrete time.

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Course overview. Brownian motion.

22 Setembro 2014, 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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