Closedness results for BMO semi-martingales and application to quadratic BSDEs

Pauline Barrieu; Nicolas Cazanave; Nicole El Karoui

doi:10.1016/j.crma.2008.06.010

Probability Theory

Closedness results for BMO semi-martingales and application to quadratic BSDEs
[Un résultat de fermeture pour des semi-martingales BMO et une application aux EDSRs à croissance quadratique]

Présenté par : Marc Yor

Pauline Barrieu ¹ ; Nicolas Cazanave ² ; Nicole El Karoui ²

¹ London School of Economics, Statistics department, Houghton Street, London WC2A 2AE, United Kingdom
² C.M.A.P., École polytechnique, 91128 Palaiseau cedex, France

Comptes Rendus. Mathématique, Volume 346 (2008) no. 15-16, pp. 881-886.

Résumé
Abstract

Nous donnons un résultat de fermeture pour un ensemble convexe de semi-martingales BMO, qui inclut les solutions de EDSRs à croissance quadratique. Nous en déduisons des résultats de convergence et de stabilité monotone pour les EDSRs à croissance quadratique.

We give a closedness result for a convex set of BMO semi-martingales, that contains solutions to quadratic BSDEs. We deduce convergence and monotone stability results for quadratic BSDEs.

Reçu le : 2007-09-24
Accepté le : 2008-06-27
Publié le : 2008-07-26

DOI : 10.1016/j.crma.2008.06.010

Affiliations des auteurs :

Pauline Barrieu ¹ ; Nicolas Cazanave ² ; Nicole El Karoui ²

¹ London School of Economics, Statistics department, Houghton Street, London WC2A 2AE, United Kingdom
² C.M.A.P., École polytechnique, 91128 Palaiseau cedex, France

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     author = {Pauline Barrieu and Nicolas Cazanave and Nicole El Karoui},
     title = {Closedness results for {BMO} semi-martingales and application to quadratic {BSDEs}},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {881--886},
     publisher = {Elsevier},
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     year = {2008},
     doi = {10.1016/j.crma.2008.06.010},
     language = {en},
}

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Pauline Barrieu; Nicolas Cazanave; Nicole El Karoui. Closedness results for BMO semi-martingales and application to quadratic BSDEs. Comptes Rendus. Mathématique, Volume 346 (2008) no. 15-16, pp. 881-886. doi : 10.1016/j.crma.2008.06.010. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2008.06.010/

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