After introducing a new concept, the notion of
$\mathscr{E}$-martingale, we extend the well-known Doob inequality (for $1 <
p < +\infty)$ and the Burkholder–Davis–Gundy inequalities (for
$p = 2$) to $\mathscr{E}$-martingales. By means of these inequalities, we give
sufficient conditions for the closedness of a space of stochastic integrals
with respect to a fixed $\mathbb{R}^d$-valued semimartingale, a question which
arises naturally in the applications to financial mathematics. We also provide
a necessary and sufficient condition for the existence and uniqueness of the
Föllmer–Schweizer decomposition.
@article{1022855653,
author = {Choulli, Tahir and Krawczyk, Leszek and Stricker, Christophe},
title = {${\scr E}$-martingales and their applications in mathematical
finance},
journal = {Ann. Probab.},
volume = {26},
number = {1},
year = {1998},
pages = { 853-876},
language = {en},
url = {http://dml.mathdoc.fr/item/1022855653}
}
Choulli, Tahir; Krawczyk, Leszek; Stricker, Christophe. ${\scr E}$-martingales and their applications in mathematical
finance. Ann. Probab., Tome 26 (1998) no. 1, pp. 853-876. http://gdmltest.u-ga.fr/item/1022855653/