no. 15-16
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

Barrieu, Pauline1 ; Cazanave, Nicolas2 ; El Karoui, Nicole2
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, Tome 346 (2008) no. 15-16, pp. 881-886.

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 :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2008.06.010
Barrieu, Pauline 1 ; Cazanave, Nicolas 2 ; El Karoui, Nicole 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 
@article{CRMATH_2008__346_15-16_881_0,
     author = {Barrieu, Pauline and Cazanave, Nicolas and El Karoui, Nicole},
     title = {Closedness results for {BMO} semi-martingales and application to quadratic {BSDEs}},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {881--886},
     publisher = {Elsevier},
     volume = {346},
     number = {15-16},
     year = {2008},
     doi = {10.1016/j.crma.2008.06.010},
     language = {en},
     url = {http://www.numdam.org/articles/10.1016/j.crma.2008.06.010/}
}
TY  - JOUR
AU  - Barrieu, Pauline
AU  - Cazanave, Nicolas
AU  - El Karoui, Nicole
TI  - Closedness results for BMO semi-martingales and application to quadratic BSDEs
JO  - Comptes Rendus. Mathématique
PY  - 2008
SP  - 881
EP  - 886
VL  - 346
IS  - 15-16
PB  - Elsevier
UR  - http://www.numdam.org/articles/10.1016/j.crma.2008.06.010/
DO  - 10.1016/j.crma.2008.06.010
LA  - en
ID  - CRMATH_2008__346_15-16_881_0
ER  - 
%0 Journal Article
%A Barrieu, Pauline
%A Cazanave, Nicolas
%A El Karoui, Nicole
%T Closedness results for BMO semi-martingales and application to quadratic BSDEs
%J Comptes Rendus. Mathématique
%D 2008
%P 881-886
%V 346
%N 15-16
%I Elsevier
%U http://www.numdam.org/articles/10.1016/j.crma.2008.06.010/
%R 10.1016/j.crma.2008.06.010
%G en
%F CRMATH_2008__346_15-16_881_0
Barrieu, Pauline; Cazanave, Nicolas; El Karoui, Nicole. Closedness results for BMO semi-martingales and application to quadratic BSDEs. Comptes Rendus. Mathématique, Tome 346 (2008) no. 15-16, pp. 881-886. doi : 10.1016/j.crma.2008.06.010. http://www.numdam.org/articles/10.1016/j.crma.2008.06.010/

[1] Delbaen, F.; Monat, P.; Schachermayer, W.; Schweizer, M.; Stricker, C. Weighted norm inequalities and hedging in incomplete market, Finance and Stochastics, Volume 1 (1997), pp. 181-227

[2] Delbaen, F.; Schachermayer, W. A compactness principle for bounded sequences of martingales with applications, Proceedings of the Seminar of Stochastic Analysis, Random Fields and Applications, Progress in Probability, vol. 45, 1999, pp. 137-173

[3] Doléans-Dade, C.; Meyer, P.A. Inégalités de normes avec poids, Séminaire de probabilités (Strasbourg), Volume 13 (1979), pp. 313-331

[4] Hu, Y.; Imkeller, P.; Müller, M. Utility maximization in incomplete markets, Annals of Applied Probability, Volume 15 (2005), pp. 1691-1712

[5] Kazamaki, N. Continuous Exponential Martingales and BMO, Lecture Notes in Mathematics, vol. 1579, Springer-Verlag, 1994

[6] Kobylanski, M. Backward stochastic differential equations and partial differential equations with quadratic growth, Annals of Probability, Volume 28 (2000), pp. 558-602

[7] Lepeltier, J.P.; San Martin, J. Backward stochastic differential equations with continuous coefficient, Statistics and Probability Letters, Volume 32 (1997), pp. 425-430

[8] Pardoux, E.; Peng, S. Adapted solution of a backward stochastic differential equation, Systems and Control Letters, Volume 14 (1990), pp. 55-61

[9] Yor, M. Sous-espaces denses dans L1 ou H1 et representation des martingales, Séminaire de Probabilité XII, Lecture Notes in Mathematics, vol. 649, Springer-Verlag, Berlin, 1978, pp. 265-309

Cité par Sources :