Bipolar behavior of submodular, law-invariant capacities

IF 1.3 Q2 STATISTICS & PROBABILITY

Statistics & Risk Modeling Pub Date : 2021-07-01 DOI:10.1515/strm-2020-0025

M. Amarante

引用次数: 2

Abstract

Abstract In the case of a submodular, law-invariant capacity, we provide an entirely elementary proof of a result of Marinacci [M. Marinacci, Upper probabilities and additivity, Sankhyā Ser. A 61 1999, no. 3, 358–361]. As a corollary, we also show that the anticore of a continuous submodular, law-invariant nonatomic capacity has a dichotomous nature: either it is one-dimensional or it is infinite-dimensional. The results have implications for the use of such capacities in financial and economic applications.

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子模、律不变容量的双极行为

摘要在子模、律不变容量的情况下，我们提供了Marinacci结果的一个完全初等的证明[M.Marinacci，Upper probabilities and additivity，SankhyāSer.a 61 1999，no.3358-361]。作为推论，我们还证明了连续子模、律不变的非原子容量的反核具有二分法性质：要么是一维的，要么是无限维的。研究结果对在金融和经济应用中使用这种能力具有启示意义。

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

Statistics & Risk Modeling STATISTICS & PROBABILITY-

CiteScore

1.80

自引率

6.70%

发文量

期刊介绍： Statistics & Risk Modeling (STRM) aims at covering modern methods of statistics and probabilistic modeling, and their applications to risk management in finance, insurance and related areas. The journal also welcomes articles related to nonparametric statistical methods and stochastic processes. Papers on innovative applications of statistical modeling and inference in risk management are also encouraged. Topics Statistical analysis for models in finance and insurance Credit-, market- and operational risk models Models for systemic risk Risk management Nonparametric statistical inference Statistical analysis of stochastic processes Stochastics in finance and insurance Decision making under uncertainty.