An analysis of two modifications of the Petersburg game

Abstract

Two modifications of the Petersburg game are considered: (1) truncation, so that the player has a finite capital at his disposal and (2) a cost of borrowing capital, so that the player has to pay interest on the capital needed. In both cases, limit theorems for the total net gain are derived, so that it is easy to judge if the game is favourable or not.

Keywords:

• Petersburg game
• free lunch
• arbitrage possibility
• limited capital
• cost of capital
• profitability

AMS Subject Classification:

• 60F05
• 60E07