Abstract
We explore some little investigated aspects of the well known betting scheme defining coherent lower or upper previsions in terms of admissible gains. A limiting situation (lose-or-draw) where the supremum of some gain is zero is discussed, deriving a gambler’s gain evaluations and comparing the differences between the imprecise and precise prevision cases. Then, the correspondence of the betting scheme for imprecise previsions with real-world situations is analysed, showing how the gambler’s profit objectives may compel him to select certain types of bets.
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References
Crisma, L.: Introduzione alla teoria delle probabilità coerenti. EUT, Trieste (2006)
de Finetti, B.: Theory of Probability, vol. I. Wiley, London (1974)
de Cooman, G., Troffaes, M.C.M., Miranda, E.: n-Monotone lower previsions. Journal of Intelligent & Fuzzy Systems 16, 253–263 (2005)
Schervish, M.J., Seidenfeld, T., Kadane, J.B.: The fundamental theorem of prevision and asset pricing. Internat. J. Approx. Reason. 49, 148–158 (2008)
Shafer, G.: A Mathematical Theory of Evidence. Princeton University Press, Princeton (1976)
Walley, P.: Statistical Reasoning with Imprecise Probabilities. Chapman & Hall, London (1991)
Walley, P.: Measures of uncertainty in expert systems. Artificial Intelligence 83, 1–58 (1996)
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© 2010 Springer-Verlag Berlin Heidelberg
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Vicig, P. (2010). A Gambler’s Gain Prospects with Coherent Imprecise Previsions. In: Hüllermeier, E., Kruse, R., Hoffmann, F. (eds) Information Processing and Management of Uncertainty in Knowledge-Based Systems. Theory and Methods. IPMU 2010. Communications in Computer and Information Science, vol 80. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14055-6_6
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DOI: https://doi.org/10.1007/978-3-642-14055-6_6
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-14054-9
Online ISBN: 978-3-642-14055-6
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