Enterprise Risk Management (ERM) Practice Questions - Enterprise Risk Management (ERM) - Actuaries Institute Fellowship Program Exam

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Which of the following mathematical properties is REQUIRED for a risk measure ρ(X) to be classified as a 'coherent risk measure' under the Artzner et al. (1999) axioms?

Subadditivity: ρ(X + Y) ≤ ρ(X) + ρ(Y) Strict superadditivity: ρ(X + Y) > ρ(X) + ρ(Y) Quadratic scaling: ρ(λX) = λ² ρ(X) for all λ > 0 Invariance under non-linear monotone transformations: ρ(g(X)) = g(ρ(X))

Correct Answer:

Subadditivity: ρ(X + Y) ≤ ρ(X) + ρ(Y)

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