1. Effect of forget-remember mechanism on
the evolution of complex financial system
Deng Weibing, Li Wei and Cai Xu
Complexity Science Center
Central China Normal University , Wuhan , China

2. Outline: [1] Forget-remember mechanism (FRM).
[2] The herding multi-agent model.
[3] FRM on the complex financial system.
[4] Some results.
[5] Discussions and Outlook.

3. [1] The Forget-remember mechanism on spreading
take a different way by relating the message spreading to the learning process.
In the message spreading, individuals forget and remember messages as time elapses.

5. The next state of the agent depends on
the previous states,
not just only on the current state !
Different from that of the Markov-chain

6. [2] The herding multi-agent model
(i) A random dispersion of information
(ii) Herding: agents having the same state and being
linked form a cluster that makes consensual decisions
(iii) Each agent within the cluster randomly changes its state
V.M. Eguiluz and M.G. Zimmerman, Phys. Rev. Lett 85 (2000) 26

7. Ignoring the influence of
the historical actions and state

8. Actions of the agents depend on: [1] Previous actions or states:
[3] FRM on the complex financial system
Actions of the agents depend on:
[1] Previous actions or states:
Similar to the FRM
[2] Environmental influence:
State of the neighbors

9. Consider a system of N agents in a scale free network, the optional states of the agents : { 0 , 1 }
1 : posses the valuable securities. 0 : not.
0 → 1: buy the price will rise.
1 → 0: sell the price will fall.

10. Where d is the difference,
z is the market depth

11. [4] Some results:

14. Fractal structure:
Long-range correlations:

15. Discussions and outlook :
[1] Change the values of the parameters
[2] How to compare with the empirical data?
[3] The theoretical solutions

16. Acknowledgement [1] Prof. Li Wei and Prof. Cai Xu
[2] Prof. Didier Sornette
[3] China Center of Advanced Science and Technology

17. Welcome comments!
Thank You !