Hostname: page-component-76fb5796d-wq484 Total loading time: 0 Render date: 2024-04-26T07:05:00.588Z Has data issue: false hasContentIssue false
  • English
  • Français

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.
Get access Rights & Permissions [Opens in a new window]

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 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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