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