The St. Petersburg Paradox: Historical Exposition, an Application to Growth Stocks and Some Simulation Approaches The St. Petersburg Paradox: Historical Exposition, an Application to Growth Stocks and Some Simulation Approaches

Abstract. The paradox of the St. Petersburg game is one of the oldest classical problems in probability theory. The payer’s payoff is doubled as long as the coin he flips shows head; therefore the game is characterized by an infinite expectation value. This shows that no finite amount of money can be a fair entrance fee. The present contribution summarizes some attempts to resolve the para-dox and analyzes a fascinating paper in which the valuation of growth stocks is relate to the St. Petersburg game. The conclusion is that the run-up in high-tech stock price in the late of 1990’s and the subsequent declines could be avoided by an analysis and an application of St. Petersburg game. Last section concerns on some approaches to simulate the St. Petersburg paradox. The main result is that the theoretical and simulated outcomes are in agreement only if the game is played an infinite number of times, a practical impossibility