# Nonlinear expectation

Template:Single source In probability theory, a nonlinear expectation is a nonlinear generalization of the expectation. Nonlinear expectations are useful in utility theory as they more closely match human behavior than traditional expectations.Template:Cn

## Definition

A functional ${\displaystyle {\mathbb {E} }:{\mathcal {H}}\to {\mathbb {R} }}$ (where ${\displaystyle {\mathcal {H}}}$ is a vector lattice on a probability space) is a nonlinear expectation if it satisfies:[1][2]

Often other properties are also desirable, for instance convexity, subadditivity, positive homogeneity, and translative of constants.[1]

## References

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