Uncertainty orders on the sublinear expectation space

• Autorzy: Dejian Tian , Long Jiang
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Uncertainty order; Sublinear expectation; Choquet integral; Quantile function; Risk measure

Kategorie tematyczne

• 90B50: Management decision making, including multiple objectives
• 91B06: Decision theory
• 62C86: Decision theory and fuzziness

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2016
• Tom: 14
• Numer: 1
• Strony: 247-259

Daty

wydano

2016-01-01

zaakceptowano

2016-01-08

online

2016-04-23

otrzymano

2104-05-08

Twórcy

autor

Dejian Tian

• School of Sciences, China University of Mining and Technology,

autor

Long Jiang

• School of Sciences, China University of Mining and Technology,

Identyfikatory

DOI

10.1515/math-2016-0023