Exercises on Ito formula. Stochastic exponential

4 Novembro 2020, 11:30 • João Guerra

Examples and exercises on Itô formula. 

The Stochastic exponential. Examples. 

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Stochastic integrals and Itô formula

2 Novembro 2020, 10:00 • João Guerra

Distribution of the models for the Team work among the different groups. 

Stochastic integration with respect to Lévy processes. Predictable processes and sufficient conditions for the stochastic integrals to be well defined. 

Lévy-type stochastic integrals. Examples. 

The Itô formula for Poisson stochastic integrals with finite variation, for Brownian integrals with drift (Itô processes) and general Itô formula for Lévy-type stochastic integrals. 

 

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Team work discussion and exercises

28 Outubro 2020, 11:30 • João Guerra

Team work: formation of the groups, presentation of the group assignment. 

Discussion of some exercises from the exercise list. 

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Processes of finite variation. Lévy-Itô decomposition

26 Outubro 2020, 10:00 • João Guerra

Processes of finite variation. Example. 

Lévy-Itô decomposition. Example of Lévy-Itô decomposition for a finite variation process. 

Financial interpretation of the terms of Lévy-Itô decomposition. 

Finite variation and finite activity. 

Finite moments of Lévy processes. 

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Exercises

21 Outubro 2020, 11:30 • João Guerra

Exercises on Subordinators, martingales and Poisson integrals. Exercises 1.14, 1.17, 1.20. 

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