Time varying moments, regime switch, and crisis warning: The birth–death process with changing transition probability

The sub-prime crisis in the U.S. reveals the limitation of diversification strategy based on mean–variance analysis. A regime switch and a turning point can be observed using a high moment representation and time-dependent transition probability. Up–down price movements are induced by interactions among agents, which can be described by the birth–death (BD) process. Financial instability is visible by dramatically increasing 3rd to 5th moments one-quarter before and during the crisis. The sudden rising high moments provide effective warning signals of a regime-switch or a coming crisis. The critical condition of a market breakdown can be identified from nonlinear stochastic dynamics. The master equation approach of population dynamics provides a unified theory of a calm and turbulent market.