The Annals of Probability

${\scr E}$-martingales and their applications in mathematical finance

Tahir Choulli, Leszek Krawczyk, and Christophe Stricker

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Abstract

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 information

Source
Ann. Probab., Volume 26, Number 2 (1998), 853-876.

Dates
First available in Project Euclid: 31 May 2002

Permanent link to this document
https://projecteuclid.org/euclid.aop/1022855653

Digital Object Identifier
doi:10.1214/aop/1022855653

Mathematical Reviews number (MathSciNet)
MR1626523

Zentralblatt MATH identifier
0938.60032

Subjects
Primary: 60G48: Generalizations of martingales 60H05: Stochastic integrals 90A09

Keywords
Semimartingales stochastic integrals stochastic exponential reverse Hölder inequalities weighted norm inequalities Föllmer-Schweizer decompositin

Citation

Choulli, Tahir; Krawczyk, Leszek; Stricker, Christophe. ${\scr E}$-martingales and their applications in mathematical finance. Ann. Probab. 26 (1998), no. 2, 853--876. doi:10.1214/aop/1022855653. https://projecteuclid.org/euclid.aop/1022855653


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