Microscopic and kinetic models in financial markets

Modeling and Simulation in Science, Engineering and Technology

Volumn 51, Issue , 2010, Pages 51-80

  Cordier, Stephane ^a   Maldarella, Dario ^b   Pareschi, Lorenzo ^b   Piatecki, Cyrille ^a  

^a UNIVERSITÉ D'ORLÉANS   (France)

^b UNIVERSITY OF FERRARA   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 80455143378     PISSN: 21643679     EISSN: 21643725     Source Type: Book Series    
DOI: 10.1007/978-0-8176-4946-3_3     Document Type: Chapter

References (45)

1. Bouchaud, J.P., Mézard, M., Wealth condensation in a simple model of economy, Physica A, 282, (2000), 536.
2. Caldarelli, G., Marsili, M., Zhang, Y.C., Europhysics Letters 40, (1997), 476.
3. Cercignani, C., Illner, R., Pulvirenti, M., The mathematical theory of dilute gases. Springer, New-York (1994)
4. Chakraborti, A., Chakrabarti, B.K., Statistical mechanics of money: how saving propensity affects its distributions, The European Physical Journal B, 17, (2000), 167.
5. Chatterjee, A., Chakrabarti, B.K., Manna, S.S., Pareto law in a kinetic model of market with random saving propensity, Physica A, 335, (2004), 155–163.
6. Cont, B., Bouchaud, J.P., Herd behaviour and aggregate fluctuations in financial markets. Macroeconomic Dynamics, 4, (2000), 170–196.
7. Cordier, S., Pareschi L., Toscani G., On a kinetic model for a simple market economy. Journal of Statistical Physics, 120, (2005), 253–277.
8. Cordier, S., Pareschi L., Piatecki C., Mesoscopic modelling of financial markets. Journal of Statistical Physics, 134, (2009), 161–184.
9. Drăgulescu, A., Yakovenko, V.M., Statistical mechanics of money, The European Physical Journal B, 17, (2000), 723–729.
10. Düring, B., Toscani, G., Hydrodynamics from kinetic models of conservative economies, Physica A, 384, (2007), 493–506.
11. Ernst, M.H., Brito, R., Scaling solutions of inelastic Boltzmann equation with over-populated high energy tails. Journal of Statistical Physics, 109, (2002), 407–432.
12. Gabaix, X., Gopikrishnan, P., Plerou, V., Stanley, H.E., A Theory of Power-Law Distributions in Financial Market Fluctuations, Nature 423, (2003), 267–270.
13. Gibrat, R., Les in`e galit`es `economiques, Librairie du Recueil Sirey, Paris, (1931).
14. Hill, I., Taylor, R., Recent trends in dividends payments and share buy-backs, Economic Trends, 567, (2001), 42–44.
15. Huang, Z.F., Solomon, S., Stochastic multiplicative processes for financial markets. Physica A, 306, (2002), 412–422.
16. Ingersoll, J.E. Jr., Theory of Financial Decision Making, Rowman and Littlefield Publishers, Inc., (1987).
17. Ispolatov, S., Krapivsky, P.L., Redner, S., Wealth distributions in asset exchange models, The European Physical Journal B, 2, (1998), 267–276.
18. Kahneman, D., Tversky, A., Prospect theory: an analysis of decision under risk, Econometrica, (1979), 263–292.
19. Kahneman, D., Tversky, A., Choices, Values, and Frames. Cambridge University Press, Cambridge (2000).
20. Kim, G., Markowitz, H.M., Investment rules, margin and market volatility. Journal of Portfolio Management, 16, (1989), 45–52.
21. Levy, M., Levy, H., Solomon, S., A microscopic model of the stock market: Cycles, booms and crashes, Economics Letters, 45, (1994), 103–111.
22. Levy, M., Levy, H., Solomon, S., Microscopic simulation of financial markets: from investor behaviour to market phoenomena, Academic Press, London (2000).
23. Levy M., Solomon, S., Dynamical explanation for the emergence of power law in a stock market. International Journal of Modern Physics C, 7, (1996), 65–72.
24. Levy, M., Solomon, S., New evidence for the power law distribution of wealth, Physica A, 242, 90, (1997).
25. Liron, N., Rubinstein, J., Calculating the fundamental solution to linear convection-diffusion problems, SIAM Journal on Applied Mathematics 44, (1984), 493–511.
26. Lux, T., The socio-economic dynamics of speculative markets: interacting agents, chaos, and the fat tails of return distributions, Journal of Economic Behavior & Organization, 33, (1998), 143–165.
27. Lux, T., Marchesi, M., Scaling and criticality in a stochastich multi-agent model of a financial market. Nature, 397 No. 11, (1999), 498–500.
28. Lux, T., Marchesi, M., Volatility clustering in financial markets: a microscopic simulation of interacting agents, International Journal of Theoretical and Applied Finance, 3, (2000), 675–702
29. Malcai, O., Biham, O., Solomon, S., Richmond, P., Theoretical analysis and simulations of the generalized Lotka-Volterra model, Physical Review E, 66, (2002), 031102.
30. Maldarella, D., Pareschi L., Kinetic models for socio-economic dynamics of speculative markets. CMCS Report, (2009).
31. Mantegna, R.N., Stanley, H.E., An Introduction to Econophysics Correlations and Complexity in Finance, Cambridge University Press, Cambridge (2000).
32. Matthes, D., Toscani, G., On steady distributions of kinetic models of conservative economies, Journal of Statistical Physics, 130, (2008), 1087–1117.
33. Mitzenmacher, M., A Brief history of generative models for power law and lognormal distributions, Internet Mathematics, 1, No. 2, (2004), 226–251.
34. Pagan, A., The econometrics of financial markets, Journal of Empirical Finance 3, (1996), 15–102.
35. Pareto, V., Cours d’Economie Politique, Lausanne and Paris, (1897).
36. Pareschi, L., Toscani, G., Self-similarity and power-like tails in nonconservative kinetic models, Journal of Statistical Physics, 124, (2006), 747–779.
37. Plerou, V., Gopikrishnan, P., Stanley, H.E., Two-phase behaviour of financial markets, Nature, 421, (2003), 130.
38. Redner, S., Random multiplicative processes: an elementary tutorial, American Journal of Physics, (1990).
39. Samanidou, E., Zschischang, E., Stauffer, D., Lux, T., Microscopic models of financial markets, Economic working papers, 15, Christian-Albrechts-University of Kiel, Department of Economics, (2006).
40. Slanina, F., Inelastically scattering particles and wealth distribution in an open economy, Physical Review E 69, (2004), 046102.
41. Solomon, S., Richmond, P., Power laws of wealth, market order volumes and market returns, Physica A 299, (2001), 188–197.
42. Solomon, S., Stochastic Lotka-Volterra systems of competing auto-catalytic agents lead generically to truncated Pareto power wealth distribution, truncated Levy distribution of market returns, clustered volatility, booms and crashes, Computational Finance 97, eds. A-P. N. Refenes, A.N. Burgess, J.E. Moody (Kluwer Academic Publishers, Dordrecht (Hingham, MA), 1998).
43. Stigler, G.J., Public regulation of the securities market. Journal of Business, 37, (1964), 117–142.
44. Toscani, G., Kinetic Models of opinion formation, Communications in Mathematical Sciences, (2006).
45. Voit, J., The Statistical Mechanics of Financial Markets, Springer, Berlin, (2005).