Abstract
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.
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Cardin, M., Couceiro, M. (2012). An ordinal approach to risk measurement. In: Perna, C., Sibillo, M. (eds) Mathematical and Statistical Methods for Actuarial Sciences and Finance. Springer, Milano. https://doi.org/10.1007/978-88-470-2342-0_10
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DOI: https://doi.org/10.1007/978-88-470-2342-0_10
Publisher Name: Springer, Milano
Print ISBN: 978-88-470-2341-3
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