Stochastic integrals

28 Setembro 2018, 12:00 • João Guerra

Stochastic integrals: motivation, definition of stochastic integrals for simple processes and definition of stochastic integrals for processes in L^2_{a} (adapted processes in L^2). 

Examples and exercises.

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Martingales in continuous time and Brownian motion

26 Setembro 2018, 11:30 • João Guerra

Martingales in discrete time: 

Examples: Double betting system, the discounted price of an asset as a martingale in the risk-neutral probability measure. 

Martingales in continuous time: definition, examples and exercises. 

Processes defined as functions of the Brownian motion. 

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Brownian motion. Martingales in discrete time

21 Setembro 2018, 12:00 • João Guerra

Brownian motion: Basic properties. 

Conditional expectation: Basic properties. 

Martingales in discrete time: definition and example. 

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Presentation of the course. Introduction to Brownian motion

19 Setembro 2018, 11:30 • João Guerra

Presentation of the programme, assessment, bibliography. 

Brief general introduction to Brownian motion and stochastic calculus.

Brownian motion: brief history, definition and relationship with random walk. 

Brownian motion with drift: definition. 

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