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.