Lévy processes simulation

8 Novembro 2018, 10:00 • João Guerra

Lévy processes simulation. 

Simulation of: 

_Brownian motion

_Poisson processes

_General Lévy processes aproximating the jump part by a sum of indenpendent Poisson processes and replcaing the small jumps by a Brownian motion

_Gamma processes

_Variance Gamma

 

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Poisson stochastic integrals

6 Novembro 2018, 10:00 • João Guerra

Group assignments distribution. 

Poisson random measures.

Poisson stochastic integrals. Definition and properties. 

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Jumps and Poisson integration

30 Outubro 2018, 10:00 • João Guerra

Lévy processes and martingales. Examples

Jump processes, Poisson random measures and Poisson integrals. Examples. 

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Group assignments discussion

25 Outubro 2018, 10:00 • João Guerra

Group assignments discussion: formation of the groups.

What is asked in the group assignments. 

Brief presentation of the several papers that can be used as the basic reference for the group assignment. 

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Subordinators

23 Outubro 2018, 10:00 • João Guerra

Subordinators: definition, examples, characteristic exponent of subordinators. 

Subordinators and stochastic time change in Lévy processes. 

alfa-stable subordinators, 1/2-stable subordinator and Brownian hitting time, Normal inverse gaussian subordinator, the variance-Gamma process, the CGMY process, normal inverse Gaussian processes. 

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