Work

Martingale representation on enlarged filtrations: the role of the accessible jump times

Year: 2024

Type: article

Abstract: We consider a filtration G obtained as enlargement of a filtration F by a filtration H. We assume that all F-local martingales are represented by a martingale M and all H-local martingales are represented by a martingale N. M and N are not necessarily quasi-left continuous processes and their jump times may overlap. We first analyse the contribution of the accessible jump times of M and N to the Jacod dimension of the space of the H1(G)-martingales. Then we prove a martingale representation theorem on G.

Source: Stochastics

DOI: 10.1080/17442508.2024.2427725

Authors: Antonella Calzolari, Barbara Torti

Institution: University of Rome Tor Vergata

Language: English

Topic: Stochastic processes and financial applications

Subfield: Finance

Field: Economics, Econometrics and Finance

Domain: Social Sciences

Open Access status: green

Funders: Ministero dell’Istruzione, dell’Università e della Ricerca, Università degli Studi di Roma Tor Vergata

Awards: G1247448925, G5743846505, G8094597749