A representation of risk measures
نویسندگان
چکیده
Let (Ω,Σ) be a measurable space and let B(Σ) denote the Banach space of bounded, Σ-measurable functions on Ω equipped with the sup-norm. Ω is the set of states of nature and B(Σ) is the set of all (measurable) risks (see Artzner et al. [2]). A measure of risk is a mapping ρ : B(Σ) −→ R. Coherent risk measures were introduced in [5] (under the name of "upper expectations") and further studied in [2]. These are risk measures that satisfy the following four properties: (1) Translation invariance: for all f ∈ B(Σ) and for all α ∈ R,
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