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

Marco Frittelli; Marco Maggis; Ilaria Peri

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arXiv · 1201.2257

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

Marco Frittelli·Marco Maggis·Ilaria Peri

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Abstract

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

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Marco Frittelli, Marco Maggis, Ilaria Peri. 2012-09-06. Risk Measures on $\mathcal{P}(\mathbb{R})$ and Value At Risk with Probability/Loss function. https://arxiv.org/abs/1201.2257

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