On Historical Value at Risk under Distribution Uncertainty

Atsushi Iizuka¹, Yumiharu Nakano²

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

DOI: 10.4236/jmf.2015.52010                

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.

Keywords

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

Conflicts of Interest

The authors declare no conflicts of interest.

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