Law‑Invariant Return and Star‑Shaped Risk Measures
This paper introduces new characterizations for certain types of law‑invariant star‑shaped functionals, particularly those with stochastic dominance consistency. It establishes Kusuoka‑type representations for these functionals, connecting them to Value‑at‑Risk and Expected Shortfall. The results are versatile and applicable in diverse financial, insurance, and probabilistic settings.