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ISIPTA'09 -
SIXTH INTERNATIONAL SYMPOSIUM ON

IMPRECISE PROBABILITY: THEORIES AND APPLICATIONS

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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 **

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** 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: **

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