Summary
In this paper the notion of coherent prevision given by de Finetti for bounded random quantities is extended to arbitrary ones. It is shown that the main properties of de Finetti’s prevision are preserved by the extended notion and some of his conjectures on previsions of unbounded random quantities are proved. Finally, a representation theorem for finite previsions in terms of Riemann-Stieltjes integral is given for random quantities defined on a common partition of the certain event and an ensuing possible interpretation for modelling real situations is discussed.
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Work performed under the auspicies of the MURST gran «Statistical models: Probabilistic foundations and procedures for inference and decisions».
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Crisma, L., Gigante, P. & Millossovich, P. A notion of coherent revision for arbitrary random quantities. J. Ital. Statist. Soc. 6, 233 (1997). https://doi.org/10.1007/BF03178914
DOI: https://doi.org/10.1007/BF03178914