<i>g</i>-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.