Coherent risk measure
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In the field of financial economics there are a number of ways that risk can be defined; to clarify the concept theoreticians have described a number of properties that a risk measure might or might not have. A coherent risk measure is a risk measure ρ that satisfies properties of monotonicity, sub-additivity, homogeneity, and translational invariance.
Consider a random outcome X viewed as an element of a linear space of measurable functions, defined on an appropriate probability space. A functional → is said to be coherent risk measure for if it satisfies the following properties:
- Positive homogeneity
- Translation invariance