On Jensen's inequality and Holder's inequality for g-expectation

被引:4
作者
Jia, Guangyan [1 ]
机构
[1] Shandong Univ, Jinan 250100, Peoples R China
基金
中国国家自然科学基金;
关键词
Backward stochastic differential equation; g-expectation; Holder's inequality; Jensen's inequality; Minkowski's inequality; Nonlinear expectation; STOCHASTIC DIFFERENTIAL-EQUATIONS; THEOREM;
D O I
10.1007/s00013-010-0117-1
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
In this paper, we shall prove that for n > 1, the n-dimensional Jensen inequality holds for the g-expectation if and only if g is independent of y and linear with respect to z, in other words, the corresponding g-expectation must be linear. A Similar result also holds for the general nonlinear expectation defined in Coquet et al. (Prob. Theory Relat. Fields 123 (2002), 1-27 or Peng (Stochastic Methods in Finance Lectures, LNM 1856, 143-217, Springer-Verlag, Berlin, 2004). As an application of a special n-dimensional Jensen inequality for g-expectation, we give a sufficient condition for g under which the Holder's inequality and Minkowski's inequality for the corresponding g-expectation hold true.
引用
收藏
页码:489 / 499
页数:11
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