April 1998 ${\scr E}$-martingales and their applications in mathematical finance
Tahir Choulli, Leszek Krawczyk, Christophe Stricker
Ann. Probab. 26(2): 853-876 (April 1998). DOI: 10.1214/aop/1022855653
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.
Tahir Choulli. Leszek Krawczyk. Christophe Stricker. "${\scr E}$-martingales and their applications in mathematical finance." Ann. Probab. 26 (2) 853 - 876, April 1998. https://doi.org/10.1214/aop/1022855653
First available in Project Euclid: 31 May 2002
Primary: 60G48, 60H05, 90A09
Keywords: Föllmer-Schweizer decompositin, reverse Hölder inequalities, Semimartingales, stochastic exponential, stochastic integrals, weighted norm inequalities
Vol.26 • No. 2 • April 1998
Tahir Choulli, Leszek Krawczyk, Christophe Stricker "${\scr E}$-martingales and their applications in mathematical finance," The Annals of Probability, Ann. Probab. 26(2), 853-876, (April 1998)