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An ordinal approach to risk measurement

Cardin, Marta; Couceiro, Miguel (2012), An ordinal approach to risk measurement, in Perna, Cira; Sibillo, Marilena, Mathematical and Statistical Methods for Actuarial Sciences and Finance, Springer : Berlin, p. 79-86. http://dx.doi.org/10.1007/978-88-470-2342-0_10

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Type
Chapitre d'ouvrage
Date
2012
Book title
Mathematical and Statistical Methods for Actuarial Sciences and Finance
Book author
Perna, Cira; Sibillo, Marilena
Publisher
Springer
Published in
Berlin
ISBN
978-88-470-2341-3
Number of pages
408
Pages
79-86
Publication identifier
Metadata
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Author(s)
Cardin, Marta
Couceiro, Miguel
Abstract (EN)
In this short note, we aim at a qualitative framework for modeling multivariate risk. To this extent, we consider completely distributive lattices as underlying universes, and make use of lattice functions to formalize the notion of risk measure. Several properties of risk measures are translated into this general setting, and used to provide axiomatic characterizations. Moreover, a notion of quantile of a lattice-valued random variable is proposed, which is shown to retain several desirable properties of its real-valued counterpart.
Subjects / Keywords
Completely distributive lattice; invariance; continuity; Sugeno integral; risk measure; quantile