On the minimal members of convex expectations

Jianhui Huang; Guangyan Jia

doi:10.1016/j.jmaa.2010.10.072

On the minimal members of convex expectations

Jianhui Huang
, Guangyan Jia

Research output: Journal article publication › Journal article › Academic research › peer-review

3 Citations (Scopus)

Abstract

In this paper, we show that for a convex expectation E[.] defined on L1(ω,F,P), the following statements are equivalent:. (i)E is a minimal member of the set of all convex expectations defined on L1(ω,F,P);(ii)E is linear;(iii)two-dimensional Jensen inequality for E holds. In addition, we prove a sandwich theorem for convex expectation and concave expectation.

Original language	English
Pages (from-to)	42-50
Number of pages	9
Journal	Journal of Mathematical Analysis and Applications
Volume	376
Issue number	1
DOIs	https://doi.org/10.1016/j.jmaa.2010.10.072
Publication status	Published - 1 Apr 2011

Keywords

Concave expectation
Convex expectation
Jensen's inequality
Linear expectation

ASJC Scopus subject areas

Analysis
Applied Mathematics

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10.1016/j.jmaa.2010.10.072

Cite this

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AB - In this paper, we show that for a convex expectation E[.] defined on L1(ω,F,P), the following statements are equivalent:. (i)E is a minimal member of the set of all convex expectations defined on L1(ω,F,P);(ii)E is linear;(iii)two-dimensional Jensen inequality for E holds. In addition, we prove a sandwich theorem for convex expectation and concave expectation.

KW - Concave expectation

KW - Convex expectation

KW - Jensen's inequality

KW - Linear expectation

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DO - 10.1016/j.jmaa.2010.10.072

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On the minimal members of convex expectations

Abstract

Keywords

ASJC Scopus subject areas

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