$g$-Expectation of Distributions
Probability
2022-08-16 v1 Optimization and Control
Mathematical Finance
Risk Management
Abstract
We define -expectation of a distribution as the infimum of the -expectations of all the terminal random variables sharing that distribution. We present two special cases for nonlinear where the -expectation of distributions can be explicitly derived. As a related problem, we introduce the notion of law-invariant -expectation and provide its sufficient conditions. Examples of application in financial dynamic portfolio choice are supplied.
Keywords
Cite
@article{arxiv.2208.06535,
title = {$g$-Expectation of Distributions},
author = {Mingyu Xu and Zuo Quan Xu and Xun Yu Zhou},
journal= {arXiv preprint arXiv:2208.06535},
year = {2022}
}