Uniqueness of Convex-Ranged Probabilities and Applications to Risk Measures and Games
重新审视了凸值概率的唯一性定理，去掉了可数可加性和正电荷条件，得到了新的等价条件，并推广了Fréchet-Hoeffding界和Fatou性质等应用。
We revisit Marinacci’s uniqueness theorem for convex-ranged probabilities and its applications. Our approach does away with both the countable additivity and the positivity of the charges involved. In the process, we uncover several new equivalent conditions, which lead to a novel set of applications. These include extensions of the classic Fréchet–Hoeffding bounds as well as of the automatic Fatou property of law-invariant functionals. We also generalize existing results of the “collapse to the mean”-type concerning capacities and α-MEU preferences.