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Range-based risk measures and their applications

Published online by Cambridge University Press:  15 August 2023

Marcelo Brutti Righi*
Business School Federal University of Rio Grande do Sul Washington Luiz, 855, zip 90010-460, Porto Alegre, Brazil
Fernanda Maria Müller
Business School Federal University of Rio Grande do Sul Washington Luiz, 855, zip 90010-460, Porto Alegre, Brazil
Corresponding author: Marcelo Brutti Righi; Email:


We propose a family of range-based risk measures to generalize the role of value at risk (VaR) in the formulation of range value at risk (RVaR) considering other risk measures induced by a tail level. We discuss this type of measure in detail and its theoretical properties and representations. Moreover, we present a score function to evaluate the forecasts of these measures. In order to present the proposed concepts in an applied way, we performed illustrations using Monte Carlo simulations and real financial data.

Research Article
© The Author(s), 2023. Published by Cambridge University Press on behalf of The International Actuarial Association

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