Law-invariant return and star-shaped risk measures

IF 1.9 2区 经济学 Q2 ECONOMICS
Roger J.A. Laeven , Emanuela Rosazza Gianin , Marco Zullino
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引用次数: 0

Abstract

This paper presents novel characterization results for classes of law-invariant star-shaped functionals. We begin by establishing characterizations for positively homogeneous and star-shaped functionals that exhibit second- or convex-order stochastic dominance consistency. Building on these characterizations, we proceed to derive Kusuoka-type representations for these functionals, shedding light on their mathematical structure and intimate connections to Value-at-Risk and Expected Shortfall. Furthermore, we offer representations of general law-invariant star-shaped functionals as robustifications of Value-at-Risk. Notably, our results are versatile, accommodating settings that may, or may not, involve monotonicity and/or cash-additivity. All of these characterizations are developed within a general locally convex topological space of random variables, ensuring the broad applicability of our results in various financial, insurance and probabilistic contexts.

收益不变定律和星形风险度量
本文提出了规律不变星形函数类的新表征结果。我们首先建立了表现出二阶或凸阶随机支配一致性的正均质星形函数的特征。在这些特征的基础上,我们进而推导出这些函数的 Kusuoka 型表示,揭示了它们的数学结构以及与风险价值和预期缺口的密切联系。此外,我们还提供了一般规律不变星形函数的表示,作为风险价值的稳健化。值得注意的是,我们的结果具有通用性,可适用于可能涉及或可能不涉及单调性和/或现金加成性的情况。所有这些特征都是在随机变量的一般局部凸拓扑空间中提出的,从而确保了我们的结果在各种金融、保险和概率环境中的广泛适用性。
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
Insurance Mathematics & Economics
Insurance Mathematics & Economics 管理科学-数学跨学科应用
CiteScore
3.40
自引率
15.80%
发文量
90
审稿时长
17.3 weeks
期刊介绍: Insurance: Mathematics and Economics publishes leading research spanning all fields of actuarial science research. It appears six times per year and is the largest journal in actuarial science research around the world. Insurance: Mathematics and Economics is an international academic journal that aims to strengthen the communication between individuals and groups who develop and apply research results in actuarial science. The journal feels a particular obligation to facilitate closer cooperation between those who conduct research in insurance mathematics and quantitative insurance economics, and practicing actuaries who are interested in the implementation of the results. To this purpose, Insurance: Mathematics and Economics publishes high-quality articles of broad international interest, concerned with either the theory of insurance mathematics and quantitative insurance economics or the inventive application of it, including empirical or experimental results. Articles that combine several of these aspects are particularly considered.
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