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

@article{CRMATH_2008__346_15-16_881_0,
     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},
     volume = {346},
     number = {15-16},
     year = {2008},
     doi = {10.1016/j.crma.2008.06.010},
     language = {en},
}

TY  - JOUR
AU  - Pauline Barrieu
AU  - Nicolas Cazanave
AU  - Nicole El Karoui
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
DO  - 10.1016/j.crma.2008.06.010
LA  - en
ID  - CRMATH_2008__346_15-16_881_0
ER  -

%0 Journal Article
%A Pauline Barrieu
%A Nicolas Cazanave
%A Nicole El Karoui
%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
%R 10.1016/j.crma.2008.06.010
%G en
%F CRMATH_2008__346_15-16_881_0

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/

Bibliographie
Cité par

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

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

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

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

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

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

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

[9] M. Yor 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

Stefan Ankirchner; Alexander Fromm; Thomas Kruse; Alexandre Popier Optimal position targeting via decoupling fields, The Annals of Applied Probability, Volume 30 (2020) no. 2 | DOI:10.1214/19-aap1511
Martin Herdegen; Johannes Muhle-Karbe; Dylan Possamaï Equilibrium Asset Pricing with Transaction Costs, SSRN Electronic Journal (2019) | DOI:10.2139/ssrn.3326085
Antonis Papapantoleon; Dylan Possamaï; Alexandros Saplaouras Stability results for martingale representations: The general case, Transactions of the American Mathematical Society, Volume 372 (2019) no. 8, p. 5891 | DOI:10.1090/tran/7880
Khaled Bahlali; M’hamed Eddahbi; Youssef Ouknine Quadratic BSDE with $L^{2}$ -terminal data: Krylov’s estimate, Itô–Krylov’s formula and existence results, The Annals of Probability, Volume 45 (2017) no. 4 | DOI:10.1214/16-aop1115
Dylan Possamai; Nabil Kazi-Tani; Chao Zhou Quadratic BSDEs with jumps: a fixed-point approach, Electronic Journal of Probability, Volume 20 (2015) no. none | DOI:10.1214/ejp.v20-3363
B. Chikvinidze; M. Mania New Proofs of Some Results on Bounded Mean Oscillation Martingales Using Backward Stochastic Differential Equations, Journal of Theoretical Probability, Volume 27 (2014) no. 4, p. 1213 | DOI:10.1007/s10959-013-0524-x
Stefan Ankirchner; Peter Imkeller; Alexandre Popier On measure solutions of backward stochastic differential equations, Stochastic Processes and their Applications, Volume 119 (2009) no. 9, p. 2744 | DOI:10.1016/j.spa.2009.02.003

Cité par 7 documents. Sources : Crossref

Commentaires - Politique