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}
}
  • Mingyu XuZ. XuX. Zhou
  • Published 13 August 2022
  • Mathematics
  • Probability, Uncertainty and Quantitative Risk
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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