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

Operations Research, Forthcoming

20 Pages Posted: 6 Sep 2016 Last revised: 23 Jan 2018

See all articles by Xue Dong He

Xue Dong He

The Chinese University of Hong Kong - Department of Systems Engineering and Engineering Management

Xianhua Peng

Peking University - HSBC School of Business

Date Written: January 22, 2018

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.

Keywords: Capital Adequacy Tests; Value-At-Risk; Surplus-Invariance; Conicity; Positive Homogeneity; Numeraire-Invariance

JEL Classification: D81, G18, G28, G32, K23

Suggested Citation

He, Xue Dong and Peng, Xianhua, Surplus-Invariant, Law-Invariant, and Conic Acceptance Sets Must Be the Sets Induced by Value-at-Risk (January 22, 2018). Operations Research, Forthcoming, Available at SSRN: https://ssrn.com/abstract=2834259 or http://dx.doi.org/10.2139/ssrn.2834259

Xue Dong He (Contact Author)

The Chinese University of Hong Kong - Department of Systems Engineering and Engineering Management ( email )

505 William M.W. Mong Engineering Building
The Chinese University of Hong Kong, Shatin, N.T.
Hong Kong
Hong Kong

HOME PAGE: http://https://sites.google.com/site/xuedonghepage/home

Xianhua Peng

Peking University - HSBC School of Business ( email )

University Town
Shenzhen, 518055
China

Do you have a job opening that you would like to promote on SSRN?

Paper statistics

Downloads
79
Abstract Views
807
rank
355,257
PlumX Metrics