How to avoid fragility of financial systems: Lessons from the financial crisis and st. Petersburg paradox

Author

Takayasu, Hideki

Abstract

Firstly, I point out that the financial crisis occurred in 2008 has many analogous points with a physical phenomenon of brittle fracture in the sense that it is a highly irreversible phenomenon caused by concentration of stress to the weakest point. Then, I discuss distribution of gain–loss of continuous transactions of options which can be regarded as a source of stress among financial companies. The historical problem of Saint Petersburg paradox is reviewed and it is argued that the paradox is solved by decomposing the process into a combination of a fair gamble and an accompanied financial option. By generalizing this fair gamble it is shown that the gain–loss distribution in this problem is closely related to the distribution of gain–loss of business firms in the real world. Finally, I pose a serious question to the ordinary way of financing money to business firms with compound interest rates. Instead we introduce a new way of financing business firms without applying prefixed interest rates, in which financial stress is shared by all involved firms. This method is expected to reduce the risk of both financial firms and business firms, and is applicable even in the non-growing society.