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arXiv · 2208.06535

$g$-Expectation of Distributions

Mingyu Xu·Zuo Quan Xu·Xun Yu Zhou
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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.

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BibTeXRIS

Mingyu Xu, Zuo Quan Xu, Xun Yu Zhou. 2022-08-13. $g$-Expectation of Distributions. https://arxiv.org/abs/2208.06535

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