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.
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Authors addresses:
Renato Pelessoni
University of Trieste
P.le Europa n.1
I - 34127 Trieste
Italy
Paolo Vicig
Paolo Vicig
Universita' di Trieste,
Dipartimento di Matematica Applicata "B. de Finetti",
Piazzale Europa, 1
I - 34127, Trieste, Italy
Fax: ++39 040 54209
Phone: ++39 040 5587108
E-mail addresses:
| Renato Pelessoni | renato.pelessoni@econ.units.it |
| Paolo Vicig | paolo.vicig@econ.units.it |
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