Research ArticleOpen AccessGoogle Scholar indexed
On Historical Value at Risk under Distribution Uncertainty
Informatix Inc., Kanagawa, Japan
Tokyo Institute of Technology, Tokyo, Japan
- 1 Informatix Inc., Kanagawa, Japan
- 2 Tokyo Institute of Technology, Tokyo, Japan
Journal of Mathematical Finance·Volume 05 (2015)·Pages 113–115·Published 30 March 2015·DOI10.4236/jmf.2015.52010
Copy link · social · email
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.
KeywordsValue-at-RiskSublinear ExpectationCapacitiesGlivenko-Cantelli Lemma
- McNeil, A. J., Frey, R. and Embrechts, P. (2005) Quantitative Risk Management: Concepts, Techniques and Tools. Princeton University Press, Princeton.
- Föllmer, H. and Schied, A. (2004) Stochastic Finance: An Introduction in Discrete Time. 2nd Edition, Walter de Gruyter, Berlin. http://dx.doi.org/10.1515/9783110212075
- Knight, F.H. (1921) Risk, Uncertainty, and Profit. Houghton Mifflin, Boston.
- Peng, S. (2006) G-Expectation, G-Brownian Motion and Related Stochastic Calculus of Itô’s type, In: Benth, F.E., et al., Eds., Stochastic Analysis and Applications: The Abel Symposium 2005, Springer-Verlag, Berlin, 541-567.
- Peng, S. (2010) Nonlinear Expectations and Stochastic Calculus under Uncertainty. arXiv:1002.4546[math.PR]
- Denneberg, D. (1994) Non-Additive Measure and Integral. Kluwer Academic Publishers, Dordrecht. http://dx.doi.org/10.1007/978-94-017-2434-0
- Chen, Z. (2010) Strong Laws of Large Numbers for Capacities. arXiv:1006.0749[math.PR]