G-expectation of Distributions

Mingyu Xu; Zuoquan Xu; Xunyu Zhou

doi:10.3934/puqr.2022021

G-expectation of Distributions

Mingyu Xu, Zuoquan Xu, Xunyu Zhou

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

Abstract

We define g-expectation of a distribution as the infimum of the g-expectations of all the terminal random variables sharing that distribution. We present two special cases for nonlinear g where the g-expectation of distributions can be explicitly derived. As a related problem, we introduce the notion of law-invariant g-expectation and provide its sufficient conditions. Examples of application in financial dynamic portfolio choice are supplied.

Original language	English
Pages (from-to)	385-404
Number of pages	20
Journal	Probability, Uncertainty and Quantitative Risk
Volume	7
Issue number	4
DOIs	https://doi.org/10.3934/puqr.2022021
Publication status	Published - Dec 2022

Keywords

BSDE
Cost efficiency
g-expectation
Law-invariance
Portfolio selection
Probability distribution

ASJC Scopus subject areas

Statistics and Probability
Applied Mathematics
Statistics, Probability and Uncertainty

More information

10.3934/puqr.2022021

http://hdl.handle.net/10397/99073

Cite this

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title = "G-expectation of Distributions",

abstract = "We define g-expectation of a distribution as the infimum of the g-expectations of all the terminal random variables sharing that distribution. We present two special cases for nonlinear g where the g-expectation of distributions can be explicitly derived. As a related problem, we introduce the notion of law-invariant g-expectation and provide its sufficient conditions. Examples of application in financial dynamic portfolio choice are supplied.",

keywords = "BSDE, Cost efficiency, g-expectation, Law-invariance, Portfolio selection, Probability distribution",

author = "Mingyu Xu and Zuoquan Xu and Xunyu Zhou",

note = "Funding Information: The authors thank two anonymous referees for their comments. Zuo Quan Xu acknowledges financial support from the NSFC (Grant No. 11971409), The Hong Kong RGC (GRF, Grant No. 15202421), The PolyU-SDU Joint Research Center on Financial Mathematics, The CAS AMSS-POLYU Joint Laboratory of Applied Mathematics, and The Hong Kong Polytechnic University. Xun Yu Zhou acknowledges financial support through a start-up grant and the Nie Center for Intelligent Asset Management at Columbia University. Publisher Copyright: {\textcopyright} Shandong University and AIMS, LLC.",

year = "2022",

month = dec,

doi = "10.3934/puqr.2022021",

language = "English",

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N2 - We define g-expectation of a distribution as the infimum of the g-expectations of all the terminal random variables sharing that distribution. We present two special cases for nonlinear g where the g-expectation of distributions can be explicitly derived. As a related problem, we introduce the notion of law-invariant g-expectation and provide its sufficient conditions. Examples of application in financial dynamic portfolio choice are supplied.

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KW - Cost efficiency

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JF - Probability, Uncertainty and Quantitative Risk

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G-expectation of Distributions

Abstract

Keywords

ASJC Scopus subject areas

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