# Nonlinear expectation

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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 (where 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]}

## Examples

- Expected value
- Choquet expectation
- g-expectation
- If is a risk measure then defines a nonlinear expectation

## References

- ↑
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