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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

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.

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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

Information

Published: April 1998
First available in Project Euclid: 31 May 2002

zbMATH: 0938.60032
MathSciNet: MR1626523
Digital Object Identifier: 10.1214/aop/1022855653

Subjects:
Primary: 60G48, 60H05, 90A09

Rights: Copyright © 1998 Institute of Mathematical Statistics

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Vol.26 • No. 2 • April 1998
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