# g-expectation of distributions

@article{Xu2022gexpectationOD, title={g-expectation of distributions}, author={Mingyu Xu and Zuo Quan Xu and Xun Yu Zhou}, journal={Probability, Uncertainty and Quantitative Risk}, year={2022} }

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 de-rived. 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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