Roles of capital flow on the stability of a market system

• We model the capital flow in financial markets based on the Heston model and recycled noises.
• Good agreements between the new model and real data have been found.
• The mean escape time (MET) has been analyzed in capital inflow and outflow, respectively.
• The non-monotonic behaviors have been observed in the behaviors of MET versus delay time or rate of capital flow.

The roles of capital flow in an ensemble composed of sub-markets are investigated. A modified Heston model and recycled noises are employed to describe the dynamics of stock price and capital flow in the ensemble, respectively. The mean escape times of two sub-markets with a cubic nonlinearity are calculated by using numerical simulation. The results evidence that (i) there is a worst delay time or rate of capital inflow concerning the minimal stability of stock price and an optimal delay time or rate of capital outflow concerning the maximal stability of stock price when λ≤0λ≤0 (λλ denotes strength of correlation between two Wiener processes of the stock price and the volatility); (ii) when λ>0λ>0, the stability of stock price is maximally enhanced by an optimal delay time or rate of capital inflow and reduced by a worst rate of capital outflow, but monotonously strengthened by delay time of capital outflow.