Author(s)

Atsushi Iizuka¹, Yumiharu Nakano²

¹Informatix Inc., Kanagawa, Japan.
²Tokyo Institute of Technology, Tokyo, Japan.

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.

Value-at-Risk, Sublinear Expectation, Capacities, Glivenko-Cantelli Lemma

Iizuka, A. and Nakano, Y. (2015) On Historical Value at Risk under Distribution Uncertainty. Journal of Mathematical Finance, 5, 113-115. doi: 10.4236/jmf.2015.52010.