TITLE:
On Historical Value at Risk under Distribution Uncertainty
AUTHORS:
Atsushi Iizuka, Yumiharu Nakano
KEYWORDS:
Value-at-Risk, Sublinear Expectation, Capacities, Glivenko-Cantelli Lemma
JOURNAL NAME:
Journal of Mathematical Finance,
Vol.5 No.2,
April
10,
2015
ABSTRACT: We investigate the asymptotics of the historical value-at-risk under capacities defined by sublinear expectations. By generalizing Glivenko-Cantelli lemma, we show that the historical value-at-risk eventually lies between the upper and lower value-at-risks quasi surely.