Surplus-Invariant Risk Measures

• 成果类型: Article
• 署名作者: Gao, Niushan; Munari, Cosimo
• 署名单位: Toronto Metropolitan University; University of Zurich; Swiss Finance Institute (SFI)
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X
• DOI: 10.1287/moor.2019.1035
• 发表日期: 2020
• 页码: 1342-1370
• 关键词: law-invariant; sets; REPRESENTATIONS; closedness; liability; PROPERTY; SPACES

摘要

This paper presents a systematic study of the notion of surplus invariance, which plays a natural and important role in the theory of risk measures and capital requirements. So far, this notion has been investigated in the setting of some special spaces of random variables. In this paper, we develop a theory of surplus invariance in its natural framework, namely, that of vector lattices. Besides providing a unifying perspective on the existing literature, we establish a variety of new results including dual representations and extensions of surplus-invariant risk measures and structural results for surplus-invariant acceptance sets. We illustrate the power of the lattice approach by specifying our results to model spaces with a dominating probability, including Orlicz spaces, as well as to robust model spaces without a dominating probability, where the standard topological techniques and exhaustion arguments cannot be applied.