Stochastic differential Equations

10 Outubro 2016, 10:00 • João Guerra

Stochastic differentuial equations: Geometric Brownian motion, Langevin equations, Ornstein-Uhlenbeck process and mean-reversion process.

Mean-Reversion analogy to AR(1) process. Financial applications: Vasicek model and Stochastic volatility model. 

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Itô formula and stochastic differential equations

6 Outubro 2016, 11:30 • João Guerra

Itô formula: examples. 

Deterministic differential equations and stochastic differential equations. 

Diffusion processes. 

The geometric Brownian motion as a solution to a SDE. 

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Itô formula

3 Outubro 2016, 10:00 • João Guerra

Stochastic integral of an adapted process: example. 

The one dimensional Itô formula: basic idea and basic formula. 

The Itô formula for Itô processes. Example. 

The multidimensional Itô formula. 

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Stochastic integral

28 Setembro 2016, 08:00 • João Guerra

Stochastic integral. 

Simple processes. Examples. 

Stochastic integrals of simpkle processes. Example.

Stochastic integral of an adapted process. 

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Martingales

26 Setembro 2016, 10:00 • João Guerra

Martingales in discrete time. 

Basic properties. Examples. 

Martingales in continuous time. Examples. 

Martingales based on the Brownian motion. Examples.

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