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Table 2 Comparison between risk measures in newsvendor problems

From: Comparing validity of risk measures on newsvendor models in open innovation perspective

Risk measures \ Model types Consistency to the four axioms for coherent risk measures
Convexity Monotonicity Translation Equivariance Positive Homogeneity
Utility Function Yes Yes No No
Stochastic Dominance It is a reference criterion.
Thus, it is not directly applicable for implementation.
Chance Constraints (or Value-at-risk) No Yes Yes Yes
Mean-risk
Analysis
Coherent Mean-deviation from quantile or mean-semideviation Yes for all of the four axioms
General Coherent Risk Measures Yes for all of the four axioms
Non-Coherent Mean-variance No No Yes No
Mean-standard deviation No No Yes Yes
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