Considering the Harmonic Sequence "Paradox"

Blavatskyy (2006) formulated a game of chance based on the harmonic series which, he suggests, leads to a St Petersburg type of paradox. In view of the importance of the St Petersburg game to decision theory, any game which leads to a St Petersburg type paradox is of interest. Blavatskyy’s game is re-examined in this article to conclude that it does not lead to a St Petersburg type paradox.Keywords: St Petersburg paradox; harmonic series; harmonic series paradoxes; decision theory and games of chance; decision theory paradoxes; expected values.

Considering the Harmonic Sequence "Paradox"

Blavatskyy (2006) formulated a game of chance based on the harmonic series which, he suggests, leads to a St Petersburg type of paradox. In view of the importance of the St Petersburg game to decision theory, any game which leads to a St Petersburg type paradox is of interest. Blavatskyy’s game is re-examined in this article to conclude that it does not lead to a St Petersburg type paradox

Considering the Harmonic Sequence "Paradox"

Blavatskyy (2006) formulated a game of chance based on the harmonic series which, he suggests, leads to a St Petersburg type of paradox. In view of the importance of the St Petersburg game to decision theory, any game which leads to a St Petersburg type paradox is of interest. Blavatskyy’s game is re-examined in this article to conclude that it does not lead to a St Petersburg type paradox

St. Petersburg Paradox and Failure Probability

The St. Petersburg paradox provides a simple paradigm for systems that show sensitivity to rare events. Here, we demonstrate a physical realization of this paradox using tensile fracture, experimentally verifying for six decades of spatial and temporal data and two different materials that the fracture force depends logarithmically on the length of the fiber. The St. Petersburg model may be useful in a variety fields where failure and reliability are critical

On the Empirical Relevance of St. Petersburg Lotteries

Expected value theory has been known for centuries to be subject to critique by St. Petersburg paradox arguments. And there is a traditional rebuttal of the critique that denies the empirical relevance of the paradox because of its apparent dependence on existence of credible offers to pay unbounded sums of money. Neither critique nor rebuttal focus on the question with empirical relevance: Do people make choices in bounded St. Petersburg games that are consistent with expected value theory? This paper reports an experiment that addresses that question

Asymmetric loss utility: an analysis of decision under risk

This paper develops a utility model for evaluating lotteries. In estimating utility, risk averse people use an asymmetric loss function. Expected utility is seen as a special case that is a good approximation of the general case in some cases. The model resolves several paradoxes and makes easily falsifiable predictions. When used in hypothesis testing, the model allows researchers to directly specify their attitudes toward risk. The model is advantageous for two reasons. First, it is based on established principles of probability; second, it resolves several well- known paradoxes.choice under uncertainty, non-expected utility theory, risk aversion, Allais paradox, Ellsberg paradox, St. Petersburg paradox, Equity Premium Puzzle, decision theory

THREE HUNDRED YEARS OF THE ST. PETERSBURG PARADOX

The St. Petersburg Paradox was first presented by Nicholas Bernoulli in 1713. It is related to a gambling game whose mathematical expected payoff is infinite, but no reasonable person would pay more than $25 to play it. In the history, a number of ideas in different areas have been developed to solve this paradox, and this report will mainly focus on mathematical perspective of this paradox. Different ideas and papers will be reviewed, including both classical ones of 18th and 19th century and some latest developments. Each model will be evaluated by simulation using Mathematica

Risky Curves: From Unobservable Utility to Observable Opportunity Sets

Most theories of risky choice postulate that a decision maker maximizes the expectation of a Bernoulli (or utility or similar) function. We tour 60 years of empirical search and conclude that no such functions have yet been found that are useful for out-of-sample prediction. Nor do we find practical applications of Bernoulli functions in major risk-based industries such as finance, insurance and gambling. We sketch an alternative approach to modeling risky choice that focuses on potentially observable opportunities rather than on unobservable Bernoulli functions.Expected utility, Risk aversion, St. Petersburg Paradox, Decisions under uncertainty, Option theory