Convex Imprecise Previsions: Basic Issues and Applications

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Convex Imprecise Previsions: Basic Issues and Applications
In this paper we study two classes of imprecise previsions, which we termed convex and centered convex previsions, in the framework of Walley’s theory of imprecise previsions. We show that convex previsions are related with a concept of convex natural estension, which is useful in correcting a large class of inconsistent imprecise probability assessments. This class is characterised by a condition of avoiding unbounded sure loss. Convexity further provides a conceptual framework for some uncertainty models and devices, like unnormalised supremum preserving functions. Centered convex previsions are intermediate between coherent previsions and previsions avoiding sure loss, and their not requiring positive homogeneity is a relevant feature for potential applications. Finally, we show how these concepts can be applied in (financial) risk measurement. Keywords imprecise previsions, convex imprecise previsions, convex natural extension, risk measures
Renato Pelessoni, Paolo Vicig
Added 04 Jul 2010
Updated 04 Jul 2010
Type Conference
Year 2003
Authors Renato Pelessoni, Paolo Vicig
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