Jensen's inequality for g-expectation: part 1

Chen, Zengjing; Kulperger, Reg; Jiang, Long

doi:10.1016/j.crma.2003.09.017

Cited by 47 publications

(31 citation statements)

References 4 publications

(12 reference statements)

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“…Chen et al [6] obtained a very interesting result: if g does not depend on y, the above generalized Jensen's inequality holds true for each convex function h if and only if g is a superhomogeneous function, i.e., g(t, λz) ≥ λg(t, z), d P × dt − a.s. for λ ∈ R and z ∈ R d . Hu [14] and Jiang [15] improved this result independently, they showed that if the above generalized Jensen's inequality holds, then g must be independent of y.…”

Section: Holds For Each Random Variable X Such That Both E[x ] and E[mentioning

confidence: 94%

Jensen’s inequality for g-convex function under g-expectation

Jia

Péng

2009

Probab. Theory Relat. Fields

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A real valued function h defined on R is called g-convex if it satisfies the "generalized Jensen's inequality" for a given g-holds for all random variables X such that both sides of the inequality are meaningful. In this paper we will give a necessary and sufficient condition for a C 2 -function being g-convex, and study some more general situations. We also study g-concave and g-affine functions, and a relation between g-convexity and backward stochastic viability property.

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Section: Holds For Each Random Variable X Such That Both E[x ] and E[mentioning

confidence: 94%

Jensen’s inequality for g-convex function under g-expectation

Jia

Péng

2009

Probab. Theory Relat. Fields

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“…Briand et al in [1] gave a counterexample to Jensen's inequality for g-expectation. Assuming that g is independent of y, Chen et al in [3] have obtained a necessary and sufficient condition under which Jensen's inequality holds for any conditional g-expectation under F t , i.e., for any concave function h : R → R and…”

Section: Introductionmentioning

confidence: 99%

On Jensen’s inequality and Hölder’s inequality for g-expectation

Jia

2010

Arch. Math.

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“…For Jensen's inequality for gexpectation associated classical BSDEs, we refer to Briand et al [1], Chen et al [2], Jiang and Chen [12], Hu [6], Jiang [11], Fan [3], Jia [9], Jia and Peng [10] and the references therein.…”

Section: Introductionmentioning

confidence: 99%

Jensen’s inequality for backward SDEs driven by G-Brownian motion

Wang

2015

Arch. Math.

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In this note, we consider Jensen's inequality for the nonlinear expectation associated with backward SDEs driven by G-Brownian motion (G-BSDEs for short). At first, we give a necessary and sufficient condition for G-BSDEs under which one-dimensional Jensen inequality holds. Second, we prove that for n > 1, the n-dimensional Jensen inequality holds for any nonlinear expectation if and only if the nonlinear expectation is linear, which is essentially due to Jia (Arch. Math. 94 (2010), 489-499). As a consequence, we give a necessary and sufficient condition for G-BSDEs under which the n-dimensional Jensen inequality holds.

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Jensen's inequality for g-expectation: part 1

Cited by 47 publications

References 4 publications

Jensen’s inequality for g-convex function under g-expectation

Jensen’s inequality for g-convex function under g-expectation

On Jensen’s inequality and Hölder’s inequality for g-expectation

Jensen’s inequality for backward SDEs driven by G-Brownian motion

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