Jensen's inequality for <i>g</i>-expectation, Part 2

Zengjing Chen; Reg Kulperger; Long Jiang

doi:10.1016/j.crma.2003.09.037

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

Zengjing Chen ¹ ; Reg Kulperger ² ; Long Jiang 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

Comptes Rendus. Mathématique, Volume 337 (2003) no. 12, pp. 797-800.

Abstract (VO)
Résumé

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.

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.

Reçu le : 2003-04-20
Accepté le : 2003-09-17
Publié le : 2003-11-14

DOI : 10.1016/j.crma.2003.09.037

Affiliations des auteurs :

Zengjing Chen ¹ ; Reg Kulperger ² ; Long Jiang 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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     title = {Jensen's inequality for \protect\emph{g}-expectation, {Part} 2},
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Zengjing Chen; Reg Kulperger; Long Jiang. Jensen's inequality for g-expectation, Part 2. Comptes Rendus. Mathématique, Volume 337 (2003) no. 12, pp. 797-800. doi : 10.1016/j.crma.2003.09.037. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2003.09.037/

Bibliographie
Cité par

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

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

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

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

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

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

Sel Ly; Nicolas Privault Stochastic ordering by $g$ -expectations, Probability, Uncertainty and Quantitative Risk, Volume 6 (2021) no. 1, pp. 61-98 | DOI:10.3934/puqr.2021004 | Zbl:1486.60035
Wenjie Song; Panyu Wu; Guodong Zhang Jensen's inequality for $g$ -expectations in general filtration spaces, Statistics Probability Letters, Volume 169 (2021), p. 8 (Id/No 108958) | DOI:10.1016/j.spl.2020.108958 | Zbl:1455.60072
Qian Lin Jensen inequality for superlinear expectations, Statistics Probability Letters, Volume 151 (2019), pp. 79-83 | DOI:10.1016/j.spl.2019.03.006 | Zbl:1459.60050
Bao Kang Yuan The application of multi-dimensional Jensen's inequality for $G$ -martingale, Stochastic Analysis and Applications, Volume 37 (2019) no. 3, pp. 499-508 | DOI:10.1080/07362994.2019.1585264 | Zbl:1488.60158
Zhaojun Zong; Feng Hu $L^{p}$ weak convergence method on BSDEs with non-uniformly Lipschitz coefficients and its applications, Proceedings of the Indian Academy of Sciences. Mathematical Sciences, Volume 126 (2016) no. 3, pp. 433-460 | DOI:10.1007/s12044-016-0276-5 | Zbl:1348.60090
Ze-Chun Hu; Zhen-Ling Wang Jensen’s inequality for backward SDEs driven by G-Brownian motion, Archiv der Mathematik, Volume 104 (2015) no. 5, p. 491 | DOI:10.1007/s00013-015-0756-3
Zhaojun Zong; Feng Hu; Chuancun Yin; Helin Wu On Jensen's inequality, Hölder's inequality, and Minkowski's inequality for dynamically consistent nonlinear evaluations, Journal of Inequalities and Applications, Volume 2015 (2015), p. 18 (Id/No 152) | DOI:10.1186/s13660-015-0677-5 | Zbl:1383.60023
Hui Zhang Properties of solution of fractional backward stochastic differential equation, Applied Mathematics and Computation, Volume 228 (2014), pp. 446-453 | DOI:10.1016/j.amc.2013.11.081 | Zbl:1364.60078
Zhaojun Zong Jensen's inequality for generalized Peng's $g$ -expectations and its applications, Abstract and Applied Analysis, Volume 2013 (2013), p. 8 (Id/No 683047) | DOI:10.1155/2013/683047 | Zbl:1279.60034
Feng Hu Dynamically consistent nonlinear evaluations with their generating functions in $L^{p}$ , Acta Mathematica Sinica. English Series, Volume 29 (2013) no. 4, pp. 815-832 | DOI:10.1007/s10114-013-1715-1 | Zbl:1271.60068
B. Yang; H. Xiao Law of large numbers under the nonlinear expectation, Proceedings of the American Mathematical Society, Volume 139 (2011) no. 10, pp. 3753-3762 | DOI:10.1090/s0002-9939-2011-10814-1 | Zbl:1230.60023
Tao Hao $g$ -variance, Acta Mathematica Sinica. English Series, Volume 26 (2010) no. 7, pp. 1345-1354 | DOI:10.1007/s10114-010-7582-0 | Zbl:1200.60045
Guangyan Jia On Jensen’s inequality and Hölder’s inequality for g-expectation, Archiv der Mathematik, Volume 94 (2010) no. 5, p. 489 | DOI:10.1007/s00013-010-0117-1
Feng Hu; Zengjing Chen Generalized Peng's $g$ -expectations and related properties, Statistics Probability Letters, Volume 80 (2010) no. 3-4, pp. 191-195 | DOI:10.1016/j.spl.2009.10.006 | Zbl:1181.60084
Sheng Jun Fan A note on Jensen's inequality for BSDEs, Acta Mathematica Sinica. English Series, Volume 25 (2009) no. 10, pp. 1681-1692 | DOI:10.1007/s10114-009-7350-1 | Zbl:1186.60051
Long Jiang A necessary and sufficient condition for probability measures dominated by $g$ -expectation, Statistics Probability Letters, Volume 79 (2009) no. 2, pp. 196-201 | DOI:10.1016/j.spl.2008.07.037 | Zbl:1157.60329
Wei Wang Maximal inequalities for $g$ -martingales, Statistics Probability Letters, Volume 79 (2009) no. 9, pp. 1169-1174 | DOI:10.1016/j.spl.2009.01.002 | Zbl:1174.60020
Sheng-Jun Fan Jensen's inequality for filtration consistent nonlinear expectation without domination condition, Journal of Mathematical Analysis and Applications, Volume 345 (2008) no. 2, pp. 678-688 | DOI:10.1016/j.jmaa.2008.04.037 | Zbl:1159.60014
Long Jiang Jensen's inequality for backward stochastic differential equations, Chinese Annals of Mathematics. Series B, Volume 27 (2006) no. 5, pp. 553-564 | DOI:10.1007/s11401-005-0077-0 | Zbl:1109.60042
Emanuela Rosazza Gianin Risk measures via $g$ -expectations, Insurance Mathematics Economics, Volume 39 (2006) no. 1, pp. 19-34 | DOI:10.1016/j.insmatheco.2006.01.002 | Zbl:1147.91346
Long Jiang Representation theorems for generators of backward stochastic differential equations and their applications, Stochastic Processes and their Applications, Volume 115 (2005) no. 12, pp. 1883-1903 | DOI:10.1016/j.spa.2005.06.008 | Zbl:1078.60043
Long Jiang; Zengjing Chen A result on the probability measures dominated by $g$ -expectation, Acta Mathematicae Applicatae Sinica. English Series, Volume 20 (2004) no. 3, pp. 507-512 | DOI:10.1007/s10255-004-0188-5 | Zbl:1055.60059
Zengjing Chen; Reg Kulperger; Long Jiang Jensen's inequality for $g$ -expectation. I, Comptes Rendus. Mathématique. Académie des Sciences, Paris, Volume 337 (2003) no. 11, pp. 725-730 | DOI:10.1016/j.crma.2003.09.017 | Zbl:1031.60014

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