Nonlinear expectation

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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 (where is a vector lattice on a probability space) is a nonlinear expectation if it satisfies:[1][2]

  1. Monotonicity: if such that then
  2. Preserving of constants: if then

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

Examples

References

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