no. 12
Probability Theory/Statistics
Jensen's inequality for g-expectation, Part 2
[L'inégalité de Jensen pour la g-espérance, 2ème partie]

Présenté par : Paul Deheuvels

Chen, Zengjing1 ; Kulperger, Reg2 ; Jiang, Long1
1 Department of Mathematics, Shandong University, Jinan, 250100, China
2 Department of Statistical and Actuarial Science, The University of Western Ontario, London, Ontario, Canada
Comptes Rendus. Mathématique, Tome 337 (2003) no. 12, pp. 797-800.

Chen et al. (C. R. Acad. Sci. Paris, Ser. I 337 (11) (2003)) a étudié l'inégalité de Jensen pour la g-espérance sous la prétention que g n'est pas fonction de (t,y). Comme suite a cette étude, nous considérons les applications de l'inégalité de Jensen dans cet article.

Chen et al. (C. R. Acad. Sci. Paris, Ser. I 337 (11) (2003)) studied a Jensen's inequality for g-expectation under the assumption that g does not depend on (t,y). In this Note we consider some applications of this inequality.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2003.09.037
Chen, Zengjing 1 ; Kulperger, Reg 2 ; Jiang, Long 1

1 Department of Mathematics, Shandong University, Jinan, 250100, China
2 Department of Statistical and Actuarial Science, The University of Western Ontario, London, Ontario, Canada 
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Chen, Zengjing; Kulperger, Reg; Jiang, Long. Jensen's inequality for g-expectation, Part 2. Comptes Rendus. Mathématique, Tome 337 (2003) no. 12, pp. 797-800. doi : 10.1016/j.crma.2003.09.037. http://www.numdam.org/articles/10.1016/j.crma.2003.09.037/

[1] Aliprantis, C.; Boder, K. Infinite Dimensional Analysis, Springer-Verlag, Berlin, 1994

[2] Briand, P.; Coquet, F.; Hu, Y.; Mémin, J.; Peng, S. A converse comparison theorem for BSDEs and related properties of g-expectation, Electron. Comm. Probab., Volume 5 (2000), pp. 101-117

[3] Chen, Z.; Kulperger, R.; Jiang, L. Jensen's inequality for g-expectation, Part I, C. R. Acad. Sci. Paris, Ser. I, Volume 337 (2003) no. 11 (in press)

[4] El Karoui, N.; Quenez, M.C. Dynamic programming and pricing of contingent claim in an incomplete market, SIAM J. Control Optim., Volume 33 (1995), pp. 29-66

[5] Peng, S. Backward stochastic differential equations and related g-expectation (El Karoui, N.; Mazliak, L., eds.), Backward Stochastic Differential Equations, Pitman Res. Notes Math. Ser., 364, 1997, pp. 141-159

[6] Revuz, D.; Yor, M. Continuous Martingales and Brownian Motion, Springer-Verlag, Berlin, 1999

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