The authors would like to thank Prof. Fabio Bellini, University Milano Bicocca, Samuel Drapeau, Humboldt University, as well as an anonymous referee for helpful discussion on this subject. MM acknowledges the financial support provided by the European Social Fund Grant.
RISK MEASURES ON P(R) AND VALUE AT RISK WITH PROBABILITY/LOSS FUNCTION
Version of Record online: 18 FEB 2013
© 2013 Wiley Periodicals, Inc.
Volume 24, Issue 3, pages 442–463, July 2014
How to Cite
Frittelli, M., Maggis, M. and Peri, I. (2014), RISK MEASURES ON P(R) AND VALUE AT RISK WITH PROBABILITY/LOSS FUNCTION. Mathematical Finance, 24: 442–463. doi: 10.1111/mafi.12028
- Issue online: 5 JUN 2014
- Version of Record online: 18 FEB 2013
- Manuscript Accepted: OCT 2012
- Manuscript Received: FEB 2012
- European Social Fund Grant
- Value at Risk;
- distribution functions;
- law invariant risk measures;
- quasi-convex functions;
- dual representation
We propose a generalization of the classical notion of the V@Rλ that takes into account not only the probability of the losses, but the balance between such probability and the amount of the loss. This is obtained by defining a new class of law invariant risk measures based on an appropriate family of acceptance sets. The V@Rλ and other known law invariant risk measures turn out to be special cases of our proposal. We further prove the dual representation of Risk Measures on .