On Jensen's inequality and Hölder's inequality for \(g\)-expectation
type: Item
instance of: scholarly article
title: On Jensen's inequality and Hölder's inequality for \(g\)-expectation
zbMATH Open document ID: 1203.60024
author: Guangyan Jia
published in: Archiv der Mathematik
publication date: 2010-06-04T00:00:00Z
review text: The author proves that, for \(n>1\), the \(n\)-dimensional Jensen's inequality holds for the \(g\)-expectation if and only if the generator \(g \equiv g(\cdot, t, y, z)\) defined on \(\Omega \times [0, T]\times \mathbb{R} \times \mathbb{R}^d\) is independent of \(y\) and linear in \(z\). Applications are made to Minkowski's and Hölder's inequalities.
Mathematics Subject Classification ID: 60E15
Mathematics Subject Classification ID: 60H10
Mathematics Subject Classification ID: 26D10
zbMATH DE Number: 5716895
zbMATH Keywords: backward stochastic differential equations
zbMATH Keywords: \(g\)-expectation
zbMATH Keywords: Jensen's inequality
zbMATH Keywords: Hölder's inequality
zbMATH Keywords: Minkowski's inequality
zbMATH Keywords: non-linear expectation
reviewed by: Andrew Dale
describes a project that uses: Coq
MaRDI profile type: Publication
full work available at URL: s00013-010-0117-1
OpenAlex ID: W1966791701
cites work: A converse comparison theorem for BSDEs and related properties of \(g\)-expectation
cites work: Ambiguity, Risk, and Asset Returns in Continuous Time
cites work: Jensen's inequality for \(g\)-expectation. I
cites work: Filtration-consistent nonlinear expectations and related \(g\)-expectations
cites work: Backward Stochastic Differential Equations in Finance
cites work: Q4085497
cites work: On Jensen's inequality for \(g\)-expectation and for nonlinear expectation
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cites work: Jensen's inequality for backward stochastic differential equations
cites work: Adapted solution of a backward stochastic differential equation
cites work: Monotonic limit theorem of BSDE and nonlinear decomposition theorem of Doob-Meyer's type
DOI: 10.1007/S00013-010-0117-1
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description: scientific article; zbMATH DE number 5716895