Generalizing Dutch Risk Measures Through Imprecise Previsions

P. Baroni, R. Pelessoni, P. Vicig

International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 17(2), 2009, 153-177



Relationships between risk measures and imprecise probability theory have received relatively limited attention in the literature. This paper contributes to filling this gap as far as Dutch risk measures are concerned. Using imprecise previsions as a starting point, a novel generalized family of Dutch risk measures is introduced, its properties with respect to several alternative consistency notions are analyzed and its advantageous features discussed. Any such measure corresponds to an imprecise prevision correcting a first-approach uncertainty measure, while preserving its consistency properties in several cases, ranging from coherence to a weak generalization of the concept of capacity. Further, it is shown that the proposed family of measures has a practical significance in the application context of insurance pricing, since, unlike the original formulation, it may ensure a risk loading to each risk taker and is even compatible with the practice of double loading in premium policies.

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