Risk Measures on and Value at Risk with Probability/Loss Function

22 Pages Posted: 11 Jun 2014

See all articles by Marco Frittelli

Marco Frittelli

University of Florence - Dipartimento di Matematica

Marco Maggis

Milano University

Ilaria Peri

University of London - Economics, Mathematics and Statistics

Date Written: July 2014

Abstract

We propose a generalization of the classical notion of the V@R 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 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 .

Keywords: Value at Risk, distribution functions, quantiles, law invariant risk measures, quasi‐convex functions, dual representation

Suggested Citation

Frittelli, Marco and Maggis, Marco and Peri, Ilaria, Risk Measures on and Value at Risk with Probability/Loss Function (July 2014). Mathematical Finance, Vol. 24, Issue 3, pp. 442-463, 2014, Available at SSRN: https://ssrn.com/abstract=2448769 or http://dx.doi.org/10.1111/mafi.12028

Marco Frittelli (Contact Author)

University of Florence - Dipartimento di Matematica ( email )

via Lombroso 6/17
50134 Firenze, I-50134
Italy

Marco Maggis

Milano University ( email )

Via C. Saldini 50
Milano, 20133
Italy

Ilaria Peri

University of London - Economics, Mathematics and Statistics ( email )

United States

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