# Uncertainty orders on the sublinear expectation space

Open Mathematics (2016)

- Volume: 14, Issue: 1, page 247-259
- ISSN: 2391-5455

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topDejian Tian, and Long Jiang. "Uncertainty orders on the sublinear expectation space." Open Mathematics 14.1 (2016): 247-259. <http://eudml.org/doc/277092>.

@article{DejianTian2016,

abstract = {In this paper, we introduce some definitions of uncertainty orders for random vectors in a sublinear expectation space. We all know that, under some continuity conditions, each sublinear expectation 𝔼 has a robust representation as the supremum of a family of probability measures. We describe uncertainty orders from two different viewpoints. One is from sublinear operator viewpoint. After giving definitions such as monotonic orders, convex orders and increasing convex orders, we use these uncertainty orders to derive characterizations for maximal distributions, G-normal distributions and G-distributions, which are the most important random vectors in the sublinear expectation space theory. On the other hand, we also establish some uncertainty orders’ characterizations from the viewpoint of probability measures and build some connections with the theory of risk measures.},

author = {Dejian Tian, Long Jiang},

journal = {Open Mathematics},

keywords = {Uncertainty order; Sublinear expectation; Choquet integral; Quantile function; Risk measure; uncertainty order; sublinear expectation; quantile function; risk measure},

language = {eng},

number = {1},

pages = {247-259},

title = {Uncertainty orders on the sublinear expectation space},

url = {http://eudml.org/doc/277092},

volume = {14},

year = {2016},

}

TY - JOUR

AU - Dejian Tian

AU - Long Jiang

TI - Uncertainty orders on the sublinear expectation space

JO - Open Mathematics

PY - 2016

VL - 14

IS - 1

SP - 247

EP - 259

AB - In this paper, we introduce some definitions of uncertainty orders for random vectors in a sublinear expectation space. We all know that, under some continuity conditions, each sublinear expectation 𝔼 has a robust representation as the supremum of a family of probability measures. We describe uncertainty orders from two different viewpoints. One is from sublinear operator viewpoint. After giving definitions such as monotonic orders, convex orders and increasing convex orders, we use these uncertainty orders to derive characterizations for maximal distributions, G-normal distributions and G-distributions, which are the most important random vectors in the sublinear expectation space theory. On the other hand, we also establish some uncertainty orders’ characterizations from the viewpoint of probability measures and build some connections with the theory of risk measures.

LA - eng

KW - Uncertainty order; Sublinear expectation; Choquet integral; Quantile function; Risk measure; uncertainty order; sublinear expectation; quantile function; risk measure

UR - http://eudml.org/doc/277092

ER -

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