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Jensen’s inequality for \(g\)-expectation. II. (English. Abridged French version) Zbl 1031.60015

Summary: In part I (see above) the authors 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.

MSC:

60E15 Inequalities; stochastic orderings

Citations:

Zbl 1031.60014
Full Text: DOI

References:

[1] Aliprantis, C.; Boder, K., Infinite Dimensional Analysis (1994), Springer-Verlag: Springer-Verlag Berlin · Zbl 0839.46001
[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., 5, 101-117 (2000) · Zbl 0966.60054
[3] Chen, Z.; Kulperger, R.; Jiang, L., Jensen’s inequality for \(g\)-expectation, Part I, C. R. Acad. Sci. Paris, Ser. I, 337, 11 (2003), in press · Zbl 1031.60014
[4] El Karoui, N.; Quenez, M. C., Dynamic programming and pricing of contingent claim in an incomplete market, SIAM J. Control Optim., 33, 29-66 (1995) · Zbl 0831.90010
[5] Peng, S., Backward stochastic differential equations and related \(g\)-expectation, (El Karoui, N.; Mazliak, L., Backward Stochastic Differential Equations. Backward Stochastic Differential Equations, Pitman Res. Notes Math. Ser., 364 (1997)), 141-159 · Zbl 0892.60066
[6] Revuz, D.; Yor, M., Continuous Martingales and Brownian Motion (1999), Springer-Verlag: Springer-Verlag Berlin · Zbl 0917.60006
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