Convex Imprecise Previsions

Convex Imprecise Previsions In this paper centered convex previsions are introduced as a special class of imprecise previsions, showing that they retain or generalise most of the relevant properties of coherent imprecise previsions but are not necessarily positively homogeneous. The broader class of convex imprecise previsions is also studied and its fundamental properties are demonstrated, introducing in particular a notion of convex natural extension which parallels that of natural extension but has a larger domain of applicability. These concepts appear to have potentially many applications. In this paper they are applied to risk measurement, leading to a general definition of convex risk measure which corresponds, when its domain is a linear space, to the one recently introduced in risk measurement literature. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Reliable Computing Springer Journals

Convex Imprecise Previsions

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Publisher
Kluwer Academic Publishers
Copyright
Copyright © 2003 by Kluwer Academic Publishers
Subject
Mathematics; Numeric Computing; Approximations and Expansions; Computational Mathematics and Numerical Analysis; Mathematical Modeling and Industrial Mathematics
ISSN
1385-3139
eISSN
1573-1340
D.O.I.
10.1023/A:1025870204905
Publisher site
See Article on Publisher Site

Abstract

In this paper centered convex previsions are introduced as a special class of imprecise previsions, showing that they retain or generalise most of the relevant properties of coherent imprecise previsions but are not necessarily positively homogeneous. The broader class of convex imprecise previsions is also studied and its fundamental properties are demonstrated, introducing in particular a notion of convex natural extension which parallels that of natural extension but has a larger domain of applicability. These concepts appear to have potentially many applications. In this paper they are applied to risk measurement, leading to a general definition of convex risk measure which corresponds, when its domain is a linear space, to the one recently introduced in risk measurement literature.

Journal

Reliable ComputingSpringer Journals

Published: Oct 4, 2004

References

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