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Enlargement of Filtration in Discrete Time Setting

When: 

Nov 6, 2017 - 1:50pm to 2:55pm

Where: 

Rettaliata Engineering Center, Room 104

Speaker: 

Monique Jeanblanc
Département de Mathématiques, Université d'Evry Val d'Essonne

Description: 

We study, in a discrete time setting, the enlargement of filtration problem. We consider martingales in some filtration \(\mathbb{F}\), and we introduce a larger filtration \(\mathbb{G}\). We show that the martingale property in the \(\mathbb{G}\) filtration is, in general, lost, and we study the Doob decomposition of \(\mathbb{F}\)-martingales when they are considered as \(\mathbb{G}\)-adapted processes. This problem is closely linked with insider trading in a financial market. 

We illustrate the study with examples. The goal is to show that results in continuous time are obtained in a very simple way in discrete time. 

This is the joint work with Christophette Blanchet-Scalliet. 

Event Type: 

Department of Applied Mathematics - Colloquia