RISK MEASURES ON math formula AND VALUE AT RISK WITH PROBABILITY/LOSS FUNCTION

Authors


  • 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.

Abstract

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 math formula.

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