Rahul Sharma (Editor)

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.

Contents

Definition

A functional E : H → R (where H is a vector lattice on a probability space) is a nonlinear expectation if it satisfies:

  1. Monotonicity: if X , Y ∈ H such that X ≥ Y then E [ X ] ≥ E [ Y ]
  2. Preserving of constants: if c ∈ R then E [ c ] = c

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

Examples

  • Expected value
  • Choquet expectation
  • g-expectation
  • If ρ is a risk measure then E [ X ] := ρ ( − X ) defines a nonlinear expectation

    • References

    Nonlinear expectation Wikipedia
    (Text) CC BY-SA


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