Sumários

Teamwork - Informations, formations of groups and brief presentation of papers/models

5 Novembro 2021, 10:00 • João Guerra

Teamwork: formation of groups and information about the teamwork.


Brief description of the papers/models for the teamwork and of the procedures and data to consider in the numerical simulations of the teamwork. 

Lévy-Itô decomposition

3 Novembro 2021, 10:00 • João Guerra

Poisson integrals. Exercises. 

Finite variation Lévy processes.
Lévy-Itô decomposition. 
Lévy-Itô decomposition of finite variation Lévy processes. 

Martingales, Poisson random measures and Poisson integrals

29 Outubro 2021, 10:00 • João Guerra

Martingales in continuous time: Basic examples with functions of Brownian motion and with processes related to Poisson processes. 

Poisson random measures: definition and properties. 
Poisson integrals: Definition, basic properties and examples. 

Subordinators - conclusion

27 Outubro 2021, 10:00 • João Guerra

Subordinators - conclusion. The variance-gamma process.

The CGMY process.
Exercises. 
Discussion of completeness/incompleteness of markets, random sources and the Meta-theorem for completeness and arbitrage free markets. 

Subordinators

22 Outubro 2021, 10:00 • João Guerra

Subordinators. 

Examples. 
The Laplace exponent and the characteristic exponent. 
Subordinators in time changes of Lévy processes. Examples.