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A limit theorem which clarifies the ‘Petersburg Paradox'

Published online by Cambridge University Press:  14 July 2016

Anders Martin-Löf
Anders Martin-Löf*
Affiliation:
Folksam Insurance Co.
*
∗Postal address: The Folksam Group, Box 20500, S-10460 Stockholm, Sweden.
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Abstract

The total gain, SN, in N successive Petersburg games is considered, and a limit theorem for SN/N – n when N = 2n and n → ∞is proved. The limit distribution can be determined numerically with good accuracy, and this fact provides a simple rule of thumb for determining a premium for the game, which is safe from the point of view of the casino.

Keywords

PETERSBURG GAMEQUASI-STABLE DISTRIBUTIONPREMIUM VALUE
Type
Research Papers
Information
Journal of Applied Probability , Volume 22 , Issue 3 , September 1985 , pp. 634 - 643
Copyright
Copyright © Applied Probability Trust 1985 

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References

[1] Bernoulli, D. (1738) Specimen theoriae novae de mensura sortis. Comm. Acad. Sci. Imp. Petropolitanae 5, 175–192. (German translation by A. Pringsheim: Versuch einer neuen Theorie der Wertbestimmung von Glucksfällen, Verlag von Duncker & Humblot, Leipzig, 1896.)Google Scholar
[2] Feller, W. (1957), (1966) An Introduction to Probability Theory and its Applications, vols 1 and 2, Wiley, New York.Google Scholar
[3] Lévy, P. (1937) Théorie de l'addition des variables aléatoires. Gauthier-Villars, Paris.Google Scholar