2017/07/18 by Xue Dong He, He, Xue Dong, Xianhua Peng +1
Economics, Econometrics and Finance · #46N30 #47N30 #62G35 #91B30 #91Gxx #FOS: Economics and business #General Finance (q-fin.GN) #Mathematical Finance (q-fin.MF) #Risk Management (q-fin.RM) #msc:46N30 #msc:47N30 #msc:62G35 #msc:91B30 #msc:91Gxx #q-fin.GN #q-fin.MF #q-fin.RM
paper · pdf · doi:10.48550/arxiv.1707.05596
20 pages, 0 figures
arxiv created 2018/01/23 · arxiv updated 2018/01/24
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.