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arXiv · 1707.05596

Surplus-Invariant, Law-Invariant, and Conic Acceptance Sets Must be the Sets Induced by Value-at-Risk

Xue Dong He·Xianhua Peng
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Abstract

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.

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Xue Dong He, Xianhua Peng. 2018-01-23. Surplus-Invariant, Law-Invariant, and Conic Acceptance Sets Must be the Sets Induced by Value-at-Risk. https://arxiv.org/abs/1707.05596

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