Uniqueness of Convex-Ranged Probabilities and Applications to Risk Measures and Games

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-03-27 DOI:10.1287/moor.2023.0015

M. Amarante, Felix-Benedikt Liebrich, Cosimo Munari

引用次数: 0

Abstract

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.

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凸范围概率的唯一性及其在风险度量和博弈中的应用

我们重温了马林纳奇的凸范围概率唯一性定理及其应用。我们的方法摒弃了相关电荷的可数可加性和正性。在此过程中，我们发现了几个新的等价条件，并由此产生了一系列新颖的应用。其中包括经典的弗雷谢特-霍夫定边界的扩展，以及定律不变函数的自动法图性质。我们还概括了有关容量和 α-MEU 偏好的 "向均值坍缩 "型现有结果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.