FOURTH INTERNATIONAL SYMPOSIUM ON
IMPRECISE PROBABILITIES AND THEIR APPLICATIONS
Carnegie Mellon University
Pittsburgh, PA, USA
July 20-23 2005

ISIPTA'05 ELECTRONIC PROCEEDINGS

Sebastian Maass

On Coherent Variability Measures and Conditioning

Abstract

Coherent upper and lower previsions are becoming more and more popular as a mathematical model for robust valuations under uncertainty. Likewise, the mathematically equivalent class of coherent risk measures is attracting a lot attention in mathematical finance. In this paper, we show that a misinterpretation of upper previsions demands a closer examination of the basis of the theory of imprecise previsions. As a consequence, we obtain a new interpretation of coherent lower previsions as fair prices, a class of coherent variability measures, and a new type of conditioning for coherent lower previsions.

Keywords. Coherent previsions, coherent risk measures, variability measures, fair price, conditioning.

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Authors addresses:

Departement Mathematik
ETH Zurich
ETH-Zentrum, HG G 51.2 - Raemistrasse 101
8092 Zurich
Switzerland

E-mail addresses:

Sebastian Maass sebastian.maass@math.ethz.ch


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