English

Risk Measures on $\mathcal{P}(\mathbb{R})$ and Value At Risk with Probability/Loss function

Risk Management 2012-09-07 v4 Probability

Abstract

We propose a generalization of the classical notion of the V@RλV@R_{\lambda} 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@RλV@R_{\lambda} 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 P(\mathcal{P}(% \mathbb{R}).

Keywords

Cite

@article{arxiv.1201.2257,
  title  = {Risk Measures on $\mathcal{P}(\mathbb{R})$ and Value At Risk with Probability/Loss function},
  author = {Marco Frittelli and Marco Maggis and Ilaria Peri},
  journal= {arXiv preprint arXiv:1201.2257},
  year   = {2012}
}
R2 v1 2026-06-21T20:03:04.546Z