[1] The common use of nonlinear expectations is in assessing risks under uncertainty.
Generally, nonlinear expectations are categorized into sub-linear and super-linear expectations dependent on the additive properties of the given sets.
Much of the study of nonlinear expectation is attributed to work of mathematicians within the past two decades.
) is a nonlinear expectation if it satisfies:[2][3][4] The complete consideration of the given set, the linear space for the functions given that set, and the nonlinear expectation value is called the nonlinear expectation space.
Often other properties are also desirable, for instance convexity, subadditivity, positive homogeneity, and translative of constants.