When banks engage in financial market transactions they get exposed to two different types of risk: event risk and behavioural risk. When it comes to analyzing risk situations, two different types can be identified: stochastic risk management and strategic risk management. Event risk can best be analyzed by using the stochastic approach. In contrast, behavioural risk can best be analyzed by using the strategic approach. The mathematical instrument to analyze strategic interactions of the players involved is game theory. However, now behavioural risk is being analyzed using the stochastic approach. In addition, based on historical data analysis the stochastic concepts are applied to determine all kinds of financial decisions. As a result, many banks and financial intermediaries get into trouble due to neglect of the proper risk management concepts. The paper shows that game theory may become fruitful in handling behavioural risks.