Surplus-Invariant, Law-Invariant, and Conic Acceptance Sets Must Be the Sets is induced by value at Risk

• 成果类型: Article
• 署名作者: He, Xue Dong; Peng, Xianhua
• 署名单位: Chinese University of Hong Kong; Peking University; Peking University Shenzhen Graduate School (PKU Shenzhen)
• 刊物名称: OPERATIONS RESEARCH
• ISSN/ISSBN: 0030-364X
• DOI: 10.1287/opre.2018.1743
• 发表日期: 2018
• 页码: 1268-1275
• 关键词: regulatory arbitrage; liability

摘要

The regulator is interested in proposing a capital adequacy test by specifying an acceptance set for firms' capital positions at the end of a given period. This set needs to be surplus invariant; i.e., not to depend on the surplus of firms' shareholders, because the test means to protect firms' liability holders. We prove that any surplus-invariant, law-invariant, and conic acceptance set must be the set of capital positions whose value at risk at a given level is less than zero. The result still holds if we replace conicity with numeraire invariance, a property stipulating that whether a firm passes the test should not depend on the currency used to denominate its assets.