On the St. Petersburg Paradox

@article{Aase1998OnTS,
  title={On the St. Petersburg Paradox},
  author={Knut K. Aase},
  journal={Scandinavian Actuarial Journal},
  year={1998},
  volume={2001},
  pages={69 - 78}
}
  • K. Aase
  • Published 1 September 1998
  • Economics, Mathematics
  • Scandinavian Actuarial Journal
The classical St. Petersburg Paradox is discussed in terms of doubling strategies. It is claimed that what was originally thought of as a ''paradox'' can hardly be considered as very surprising today, but viewed in terms of doubling strategies, we get some results that look paradoxical, at least to the practically oriented investor. 
Ending the myth of the St Petersburg paradox
TLDR
This article argues that, in addition to the mathematical error in the original calculation of the expected value of the St Petersburg game, there are also methodological considerations which gave rise to the paradox and explains why it is the methodological correction which will dispel the myth. Expand
An Empirical Approach to the St. Petersburg Paradox
Summary The St. Petersburg game is a probabilistic thought experiment. It describes a game which seems to have infinite expected value, but which no reasonable person could be expected to pay much toExpand
The median-based resolution of the St. Petersburg paradox
Abstract The St. Petersburg Paradox contributed to establishing expected utility theory by demonstrating that decision making based on the expectation (expected value, or mean, average) leads to anExpand
Resolution of the St. Petersburg Paradox Using Von Mises’ Axiom of Randomness
In this article we will propose a completely new point of view for solving one of the most important paradoxes concerning game theory. The solution develop shifts the focus from the result to theExpand
The St. Petersburg Paradox and the Crash of High-Tech Stocks in 2000
During the late 1990s high technology growth stock prices were raised to unprecedented levels by avid stock purchasers around the world. In early 2000, share prices subsequently underwent prolongedExpand
Moral Impossibility in the Petersburg Paradox : A Literature Survey and Experimental Evidence
The Petersburg paradox has led to much thought for three centuries. This paper describes the paradox, discusses its resolutions advanced in the literature while alluding to the historical context,Expand
An analysis of two modifications of the Petersburg game
Two modifications of the Petersburg game are considered: 1. Truncation, so that the player has a finite capital at his disposal. 2. A cost of borrowing capital, so that the player has to pay interestExpand
Capitalization in the St. Petersburg game
In spite of its infinite expectation value, the St. Petersburg game is not only a gamble without supply in the real world, but also one without demand at apparently very reasonable asking prices. WeExpand
The bounded strength of weak expectations
The rational price of the Pasadena and Altadena games, introduced by Nover and Hajek (2004), has been the subject of considerable discussion. Easwaran (2008) has suggested that weak expectations —Expand
How much are you Willing to Pay to Play the Saint Petersburg Gamble
The Saint Petersburg gamble has an infinite expected payoff but few people would pay more than 32 dollars as an entrance fee to play it. In fact under reasonable conditions the maximum willingness toExpand
...
1
2
3
...

References

SHOWING 1-10 OF 19 REFERENCES
On the St. Petersburg paradox
Set theory and measure theory were developed in the early part of this century, and subsequently A. N. Kolmogoroff [1] formulated an axiomatic foundation for the mathematical theory of probability.Expand
Theory of Games and Economic Behavior
THIS book is based on the theory that the economic man attempts to maximize his share of the world's goods and services in the same way that a participant in a game involving many players attempts toExpand
Limit Theorems for the Petersburg Game
We determine all possible subsequences \(\left\{ {n_k } \right\}_{k = 1}^\infty\)of the positive integers for which the suitably centered and normalized total gain S nk in n k Petersburg games has anExpand
Exposition of a New Theory on the Measurement of Risk
EVER SINCE mathematicians first began to study the measurement of risk there has been general agreement on the following proposition: Expected values are computed by multiplying each possible gain byExpand
Admissible investment strategies in continuous trading
We consider a situation where relative prices of assets may change continuously and also have discrete jumps at random time points. The problem is the one of portfolio optimization. If the utilityExpand
RISK AVERSION IN THE SMALL AND IN THE LARGE
This paper concerns utility functions for money. A measure of risk aversion in the small, the risk premium or insurance premium for an arbitrary risk, and a natural concept of decreasing riskExpand
INVESTMENT POLICIES FOR EXPANDING BUSINESSES OPTIMAL IN A LONG-RUN SENSE
Publisher Summary Entrepreneurs have a given initial fortune and faces the following situation: during any time period, they may invest various amounts of their available fortune in variousExpand
On Cash Equivalents and Information Evaluation in Decisions Under Uncertainty Part I: Basic Theory
The monetary evaluation of decisions under uncertainty and of associated opportunities to acquire information is well known and conceptually straightforward when utility is linear in money. ThisExpand
An Introduction To Probability Theory And Its Applications
TLDR
A First Course in Probability (8th ed.) by S. Ross is a lively text that covers the basic ideas of probability theory including those needed in statistics. Expand
Minimizing or maximizing the expected time to reach zero
We treat the following control problems: the process $X_1 (t)$ with Values in the interval $( { - \infty ,0} ]$ (or $[ {0,\infty } )$) is given by the stochastic differential equation \[dX_1 (t) =Expand
...
1
2
...