The St. Petersburg paradox and its applications at financial markets

Abstract

Purpose : the author appraises the use opportunities of St. Petersburg paradox in process modeling of financial assets pricing in the fractal market. Discussion : St. Petersburg paradox is the task of probability theory sphere. It plays the important role for the evolution of several scientific fields, especially mathematics, financial mathematics and economics in general. Mathematician K. Menger was first proposed to use the St. Petersburg paradox in the economic sphere. He shifted the emphasis from determination of certain gambling «fair price» on the search for an adequate descriptive model of behavior under uncertainty. In addiction the author describes the possible applications of this model in diminishing marginal utility, expected utility as a criterion for decision making under uncertainty, fundamentals of insurance and risk management. The writer offers to use the St. Petersburg paradox in modern approaches to financial modeling. Results : the author revealed that the St. Petersburg paradox has the fractal distribution. Whereas the writer considers advisable to use the fractal distribution in the financial markets simulation.