1. Complex ’ 2009 Shanghai, China Dynamic Regimes of a Multi-agent Stock Market Model Tongkui (Kevin) Yu, Honggang Li Department of Systems Science, School of Management, BNU

2. Complex 2009 Tongkui (Kevin) Yu and Honggang Li Dynamic Regime Source: www.sohu.com

3. Complex 2009 Tongkui (Kevin) Yu and Honggang Li Dynamic Regime Source: www.sohu.com

4. Complex 2009 Tongkui (Kevin) Yu and Honggang Li Motivation Aim: (1)to find an underlying mechanism producing various dynamic regimes; (2) to investigate the factors (traders ’ propensities) determining the market in which regime. Various regimes Similar trading rules Similar traders

5. Complex 2009 Tongkui (Kevin) Yu and Honggang Li Related works Many models have been built to replicate different dynamic regimes: Chiarella, C. (1992,2001,2004) Lux, T. (1995,1998,1999) Brock, W. A., Hommes, C. H. (1997, 2001) ……

6. Complex 2009 Tongkui (Kevin) Yu and Honggang Li Bottom-up modeling Consider the behavioral pattern of traders (agents) and model it as the switch probability among different groups Derive a dynamical system to approximate the market evolution So, the dynamical system has parameters for traders ’ propensities

7. Complex 2009 Tongkui (Kevin) Yu and Honggang Li Our work Follows Lux ’ s bottom up approach. Builds a multi-agent model with four kinds of dynamic regimes (fundamental equilibrium, non-fundamental equilibrium, periodicity and chaos). Concentrates on analyzing the effect of traders ’ propensities (mimetic propensity, price-chasing propensity and strategy- switching propensity) on market dynamic regimes.

8. Complex 2009 Tongkui (Kevin) Yu and Honggang Li Outline:

9. Complex 2009 Tongkui (Kevin) Yu and Honggang Li Multi-agent Stock Market Model Market components (chartists) (fundamentalists) (optimistic chartists) (pessimistic chartists)

10. Complex 2009 Tongkui (Kevin) Yu and Honggang Li Multi-agent Stock Market Model Traders behavior Modeled as the switch probability among different groups

11. Complex 2009 Tongkui (Kevin) Yu and Honggang Li Model Switch probability between n + and n − : market sentiment index : mimetic propensity : price-chasing propensity

12. Complex 2009 Tongkui (Kevin) Yu and Honggang Li Model Switch probability between n c and n f : strategy-switching propensity

13. Complex 2009 Tongkui (Kevin) Yu and Honggang Li Model Price formation

14. Complex 2009 Tongkui (Kevin) Yu and Honggang Li Multi-agent Stock Market Model Procedure:

15. Complex 2009 Tongkui (Kevin) Yu and Honggang Li Outline:

16. Complex 2009 Tongkui (Kevin) Yu and Honggang Li Stock Market Dynamical System Where: market sentiment index market rationality index p : market price

17. Complex 2009 Tongkui (Kevin) Yu and Honggang Li Outline:

18. Complex 2009 Tongkui (Kevin) Yu and Honggang Li Dynamic regimes Fundamental equilibrium

19. Complex 2009 Tongkui (Kevin) Yu and Honggang Li Dynamic regimes Symmetric non-fundamental equilibrium

20. Complex 2009 Tongkui (Kevin) Yu and Honggang Li Dynamic regimes - Periodicity

21. Complex 2009 Tongkui (Kevin) Yu and Honggang Li Dynamic regimes - Chaos

22. Complex 2009 Tongkui (Kevin) Yu and Honggang Li Dynamic regimes – an overview with bifurcation diagram

23. Complex 2009 Tongkui (Kevin) Yu and Honggang Li Dynamic regimes – an overview with phase diagram

24. Complex 2009 Tongkui (Kevin) Yu and Honggang Li Conclusion Present an underlying mechanism that gives reasonable explanations to four kinds of market regimes. Traders' behavioral propensities play an important role in determining market dynamic regimes.

25. Complex 2009 Tongkui (Kevin) Yu and Honggang Li Further research Exact parameter ranges within which different solutions occur. Parameter calibration to make the model precise enough to describe the dynamics of a real market Slow parameters and fast parameters

26. Complex 2009 Tongkui (Kevin) Yu and Honggang Li Thanks for patience ！ Suggestions welcome!