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A kinetic model for an agent based market simulation
Boltzmann-type models for price formation in the presence of behavioral aspects
1. | Department of Physics, Via Bassi, 6, 27100 Pavia, Italy |
2. | University of Pavia, Department of Mathematics, Via Ferrata 1, 27100 Pavia, Italy |
References:
[1] |
R. Bapna, W. Jank and G. Shmueli, Price formation and its dynamics in online auctions, Decision Support Systems, 44 (2008), 641-656. |
[2] |
A. Chakraborti, Distributions of money in models of market economy, Int. J. Modern Phys. C, 13 (2002), 1315-1321.
doi: 10.1142/S0129183102003905. |
[3] |
A. Chakraborti and B. K. Chakrabarti, Statistical mechanics of money: Effects of saving propensity, Eur. Phys. J. B, 17 (2000), 167-170. |
[4] |
A. Chatterjee, B. K. Chakrabarti and S. S. Manna, Pareto law in a kinetic model of market with random saving propensity, Physica A, 335 (2004), 155-163.
doi: 10.1016/j.physa.2003.11.014. |
[5] |
A. Chatterjee, S. Yarlagadda and B. K. Chakrabarti, Eds., Econophysics of Wealth Distributions, New Economic Window Series, Springer-Verlag, Milan, 2005. |
[6] |
A. Chatterjee, B. K. Chakrabarti and R. B. Stinchcombe, Master equation for a kinetic model of trading market and its analytic solution, Phys. Rev. E, 72 (2005), 026126.
doi: 10.1103/PhysRevE.72.026126. |
[7] |
S. Cordier, L. Pareschi and G. Toscani, On a kinetic model for a simple market economy, J. Stat. Phys., 120 (2005), 253-277.
doi: 10.1007/s10955-005-5456-0. |
[8] |
M. Cristelli, L. Pietronero and A. Zaccaria, Critical overview of agent-based models for economics, in Proceedings of the School of Physics E. Fermi, course CLXXVI, Varenna, 2010. E-Print: arXiv:1101.1847. |
[9] |
A. Drăgulescu and V. M. Yakovenko, Statistical mechanics of money, Eur. Phys. Jour. B, 17 (2000), 723-729. |
[10] |
B. Düring, D. Matthes and G. Toscani, Kinetic equations modelling wealth redistribution: A comparison of approaches, Phys. Rev. E, 78 (2008), 056103.
doi: 10.1103/PhysRevE.78.056103. |
[11] |
B. Düring, D. Matthes and G. Toscani, A Boltzmann type approach to the formation of wealth distribution curves, Riv. Mat. Univ. Parma, 1 (2009), 199-261. |
[12] |
D. Kahneman and A. Tversky, Prospect theory: An analysis of decision under risk, Econometrica, 47 (1979), 183-214.
doi: 10.1017/CBO9780511609220.014. |
[13] |
D. Kahneman and A. Tversky, Choices, values, and frames, American Psychologist, 39 (1984), 341-350.
doi: 10.1037/0003-066X.39.4.341. |
[14] |
M. Levy, H. Levy and S. Solomon, Microscopic Simulation of Financial Markets: From Investor Behaviour to Market Phoenomena, Academic Press, San Diego, 2000. |
[15] |
T. Lux, 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.
doi: 10.1016/S0167-2681(97)00088-7. |
[16] |
T. Lux and M. Marchesi, Volatility clustering in financial markets: A microscopic simulation of interacting agents, International Journal of Theoretical and Applied Finance, 3 (2000), 675-702.
doi: 10.1142/S0219024900000826. |
[17] |
T. Lux and M. Marchesi, Scaling and criticality in a stochastic multi-agent model of a financial market, Nature, 397 (1999), 498-500. |
[18] |
D. Maldarella and L. Pareschi, Kinetic models for socio-economic dynamics of speculative markets, Physica A, 391 (2012), 715-730.
doi: 10.1016/j.physa.2011.08.013. |
[19] |
R. N. Mantegna and H. E. Stanley, An Introduction to Econophysics Correlations and Complexity in Finance, Cambridge University Press, Cambridge, 2007. |
[20] |
D. Matthes and G. Toscani, On steady distributions of kinetic models of conservative economies, J. Stat. Phys., 130 (2008), 1087-1117.
doi: 10.1007/s10955-007-9462-2. |
[21] |
G. Naldi, L. Pareschi and G. Toscani, Eds., Mathematical Modelling of Collective Behavior in Socio-economic and Life Sciences, Birkhäuser, Boston, 2010.
doi: 10.1007/978-0-8176-4946-3. |
[22] |
L. Pareschi and G. Toscani, Interacting Multiagent Systems: Kinetic Equations and Monte Carlo Methods, Oxford University Press, Oxford, 2014. |
[23] |
L. Pareschi and G. Toscani, Wealth distribution and collective knowledge. A Boltzmann approach, Phil. Trans. R. Soc. A, 372 (2014), 20130396, 15pp.
doi: 10.1098/rsta.2013.0396. |
[24] |
F. Slanina, Inelastically scattering particles and wealth distribution in an open economy, Phys. Rev. E, 69 (2004), 046102.
doi: 10.1103/PhysRevE.69.046102. |
[25] |
G. Toscani, Kinetic models of opinion formation, Comm. Math. Scie., 4 (2006), 481-496.
doi: 10.4310/CMS.2006.v4.n3.a1. |
[26] |
J. Voit, The Statistical Mechanics of Financial Markets, Springer Verlag, Berlin, 2005. |
show all references
References:
[1] |
R. Bapna, W. Jank and G. Shmueli, Price formation and its dynamics in online auctions, Decision Support Systems, 44 (2008), 641-656. |
[2] |
A. Chakraborti, Distributions of money in models of market economy, Int. J. Modern Phys. C, 13 (2002), 1315-1321.
doi: 10.1142/S0129183102003905. |
[3] |
A. Chakraborti and B. K. Chakrabarti, Statistical mechanics of money: Effects of saving propensity, Eur. Phys. J. B, 17 (2000), 167-170. |
[4] |
A. Chatterjee, B. K. Chakrabarti and S. S. Manna, Pareto law in a kinetic model of market with random saving propensity, Physica A, 335 (2004), 155-163.
doi: 10.1016/j.physa.2003.11.014. |
[5] |
A. Chatterjee, S. Yarlagadda and B. K. Chakrabarti, Eds., Econophysics of Wealth Distributions, New Economic Window Series, Springer-Verlag, Milan, 2005. |
[6] |
A. Chatterjee, B. K. Chakrabarti and R. B. Stinchcombe, Master equation for a kinetic model of trading market and its analytic solution, Phys. Rev. E, 72 (2005), 026126.
doi: 10.1103/PhysRevE.72.026126. |
[7] |
S. Cordier, L. Pareschi and G. Toscani, On a kinetic model for a simple market economy, J. Stat. Phys., 120 (2005), 253-277.
doi: 10.1007/s10955-005-5456-0. |
[8] |
M. Cristelli, L. Pietronero and A. Zaccaria, Critical overview of agent-based models for economics, in Proceedings of the School of Physics E. Fermi, course CLXXVI, Varenna, 2010. E-Print: arXiv:1101.1847. |
[9] |
A. Drăgulescu and V. M. Yakovenko, Statistical mechanics of money, Eur. Phys. Jour. B, 17 (2000), 723-729. |
[10] |
B. Düring, D. Matthes and G. Toscani, Kinetic equations modelling wealth redistribution: A comparison of approaches, Phys. Rev. E, 78 (2008), 056103.
doi: 10.1103/PhysRevE.78.056103. |
[11] |
B. Düring, D. Matthes and G. Toscani, A Boltzmann type approach to the formation of wealth distribution curves, Riv. Mat. Univ. Parma, 1 (2009), 199-261. |
[12] |
D. Kahneman and A. Tversky, Prospect theory: An analysis of decision under risk, Econometrica, 47 (1979), 183-214.
doi: 10.1017/CBO9780511609220.014. |
[13] |
D. Kahneman and A. Tversky, Choices, values, and frames, American Psychologist, 39 (1984), 341-350.
doi: 10.1037/0003-066X.39.4.341. |
[14] |
M. Levy, H. Levy and S. Solomon, Microscopic Simulation of Financial Markets: From Investor Behaviour to Market Phoenomena, Academic Press, San Diego, 2000. |
[15] |
T. Lux, 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.
doi: 10.1016/S0167-2681(97)00088-7. |
[16] |
T. Lux and M. Marchesi, Volatility clustering in financial markets: A microscopic simulation of interacting agents, International Journal of Theoretical and Applied Finance, 3 (2000), 675-702.
doi: 10.1142/S0219024900000826. |
[17] |
T. Lux and M. Marchesi, Scaling and criticality in a stochastic multi-agent model of a financial market, Nature, 397 (1999), 498-500. |
[18] |
D. Maldarella and L. Pareschi, Kinetic models for socio-economic dynamics of speculative markets, Physica A, 391 (2012), 715-730.
doi: 10.1016/j.physa.2011.08.013. |
[19] |
R. N. Mantegna and H. E. Stanley, An Introduction to Econophysics Correlations and Complexity in Finance, Cambridge University Press, Cambridge, 2007. |
[20] |
D. Matthes and G. Toscani, On steady distributions of kinetic models of conservative economies, J. Stat. Phys., 130 (2008), 1087-1117.
doi: 10.1007/s10955-007-9462-2. |
[21] |
G. Naldi, L. Pareschi and G. Toscani, Eds., Mathematical Modelling of Collective Behavior in Socio-economic and Life Sciences, Birkhäuser, Boston, 2010.
doi: 10.1007/978-0-8176-4946-3. |
[22] |
L. Pareschi and G. Toscani, Interacting Multiagent Systems: Kinetic Equations and Monte Carlo Methods, Oxford University Press, Oxford, 2014. |
[23] |
L. Pareschi and G. Toscani, Wealth distribution and collective knowledge. A Boltzmann approach, Phil. Trans. R. Soc. A, 372 (2014), 20130396, 15pp.
doi: 10.1098/rsta.2013.0396. |
[24] |
F. Slanina, Inelastically scattering particles and wealth distribution in an open economy, Phys. Rev. E, 69 (2004), 046102.
doi: 10.1103/PhysRevE.69.046102. |
[25] |
G. Toscani, Kinetic models of opinion formation, Comm. Math. Scie., 4 (2006), 481-496.
doi: 10.4310/CMS.2006.v4.n3.a1. |
[26] |
J. Voit, The Statistical Mechanics of Financial Markets, Springer Verlag, Berlin, 2005. |
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