ISIPTA'09 - SIXTH INTERNATIONAL SYMPOSIUM ON
IMPRECISE PROBABILITY: THEORIES AND APPLICATIONS

Durham University, Department of Mathematical Sciences
Durham, United Kingdom
Tuesday 14 to Saturday 18 July 2009

ELECTRONIC PROCEEDINGS

Renato Pelessoni, Paolo Vicig, Marco Zaffalon

The Pari-Mutuel Model

Abstract

We explore generalizations of the pari-mutuel model (PMM), a formalization of an intuitive way of assessing an upper probability from a precise one. We discuss a naive extension of the PMM considered in insurance and generalize the natural extension of the PMM introduced by P. Walley and other related formulae. The results are subsequently given a risk measurement interpretation: in particular it is shown that a known risk measure, Tail Value at Risk (TVaR), is derived from the PMM, and a coherent risk measure more general than TVaR from its imprecise version. We analyze further the conditions for coherence of a related risk measure, Conditional Tail Expectation. Explicit formulae for conditioning the PMM and conditions for dilation or imprecision increase are also supplied and discussed.

Keywords. Pari-mutuel model, risk measures, natural extension, dilation, 2-monotonicity

Paper Download

The paper is availabe in the following formats:

Plenary talk : Press here to get the file of the presentation.

Authors addresses:

Renato Pelessoni
Dip. Matematica Applicata "B. de Finetti"
University of Trieste
P.le Europa n.1
I - 34127 Trieste
Italy

Paolo Vicig
P.le Europa n.1
I-34127 Trieste
Italy

Marco Zaffalon
Galleria 2
CH-6928 Manno
Switzerland

E-mail addresses:

Renato Pelessoni renato.pelessoni@econ.units.it
Paolo Vicig paolo.vicig@econ.units.it
Marco Zaffalon zaffalon@idsia.ch


[ back to the Proceedings of ISIPTA'09 home page 
Send any remarks to the following address: smc@decsai.ugr.es