Abstract
The St Petersburg Paradox revolves round the determination of a fair price for playing the St Petersburg Game. According to the original formulation, the price for the game is infinite, and, therefore, paradoxical. Although the St Petersburg Paradox can be seen as concerning merely a game, Paul Samuelson (1977) calls it a “fascinating chapter in the history of ideas”, a chapter that gave rise to a considerable number of papers over more than 200 years involving fields such as probability theory and economics. In a paper in this journal, Vivian (2013) undertook a numerical investigation of the St Petersburg Game. In this paper, the central issue of the paradox is identified as that of fair (risk-neutral) pricing, which is fundamental in economics and finance and involves important concepts such as no arbitrage, discounting, and risk-neutral measures. The model for the St Petersburg Game as set out in this paper is new and analytical and resolves the so-called pricing paradox by applying a discounting procedure. In this framework, it is shown that there is in fact no infinite price paradox, and simple formulas for obtaining a finite price for the game are also provided.
Highlights
The famous St Petersburg Game pricing paradox has, over the last 275 years, occupied many great minds, including economists such as Paul Samuelson and J.M
Our submission is that the usual formula (1.4) used in the literature on games does not give a fair price for games with a large or possibly infinite time horizon, and that the pricing principles with discounting discussed in Section 3 should be followed
Applying the concept of discounted no-arbitrage pricing − based on the accepted model for obtaining fair prices for financial assets − to the St Petersburg Game shows that there is no infinite price paradox
Summary
The famous St Petersburg Game pricing paradox has, over the last 275 years, occupied many great minds, including economists such as Paul Samuelson and J.M. Keynes, and has directly or indirectly influenced some of the work of mathematicians such as Borel (1949), and even John van Neumann. The paradox surrounding this very famous game goes back to the early 1700s. Bernoulli presented the paradox to the St Petersburg Academy in 1738, and it has attracted attention ever since. Samuelson (1977) states that the paradox “enjoys an honoured corner in the memory bank of the cultured analytic mind”. The PG concerns a single game (between a player and a bank or casino) which may last arbitrarily long, has infinite expected payoff and, according to the paradox, an infinite price.
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callMore From: South African Journal of Economic and Management Sciences
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
