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September  2015, 10(3): 543-557. doi: 10.3934/nhm.2015.10.543

Boltzmann-type models for price formation in the presence of behavioral aspects

Carlo Brugna 1, and  Giuseppe Toscani 2,

1. 

Department of Physics, Via Bassi, 6, 27100 Pavia, Italy
2. 

University of Pavia, Department of Mathematics, Via Ferrata 1, 27100 Pavia, Italy

Received  August 2014 Revised  January 2015 Published  July 2015

We introduce and discuss a new kinetic system for a financial market composed by agents that may belong to two different trader populations, whose behavior determines the price dynamic of a certain stock. Our mesoscopic description is based on the microscopic Lux--Marchesi model [16,17], and share analogies with the recent kinetic model by Maldarella and Pareschi [18], from which it differs in various points. In particular, it takes into account price acceleration, as well as a microscopic binary interaction for the exchange between the two populations of agents. Various numerical simulations show that the model can describe realistic situations, like regimes of boom and crashes, as well as the invariance of the large-time behavior with respect to the number of agents of the market.
Keywords: markets and trades, Kinetic models, opinion formation., multi-agent systems.
Mathematics Subject Classification: Primary: 35B40, 91B60; Secondary: 82C4.
Citation: Carlo Brugna, Giuseppe Toscani. Boltzmann-type models for price formation in the presence of behavioral aspects. Networks & Heterogeneous Media, 2015, 10 (3) : 543-557. doi: 10.3934/nhm.2015.10.543
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show all references

References:
[1]

Decision Support Systems, 44 (2008), 641-656. Google Scholar

[2]

Int. J. Modern Phys. C, 13 (2002), 1315-1321. doi: 10.1142/S0129183102003905.  Google Scholar

[3]

Eur. Phys. J. B, 17 (2000), 167-170. Google Scholar

[4]

Physica A, 335 (2004), 155-163. doi: 10.1016/j.physa.2003.11.014.  Google Scholar

[5]

New Economic Window Series, Springer-Verlag, Milan, 2005. Google Scholar

[6]

Phys. Rev. E, 72 (2005), 026126. doi: 10.1103/PhysRevE.72.026126.  Google Scholar

[7]

J. Stat. Phys., 120 (2005), 253-277. doi: 10.1007/s10955-005-5456-0.  Google Scholar

[8]

in Proceedings of the School of Physics E. Fermi, course CLXXVI, Varenna, 2010. E-Print: arXiv:1101.1847. Google Scholar

[9]

Eur. Phys. Jour. B, 17 (2000), 723-729. Google Scholar

[10]

Phys. Rev. E, 78 (2008), 056103. doi: 10.1103/PhysRevE.78.056103.  Google Scholar

[11]

Riv. Mat. Univ. Parma, 1 (2009), 199-261.  Google Scholar

[12]

Econometrica, 47 (1979), 183-214. doi: 10.1017/CBO9780511609220.014.  Google Scholar

[13]

American Psychologist, 39 (1984), 341-350. doi: 10.1037/0003-066X.39.4.341.  Google Scholar

[14]

Academic Press, San Diego, 2000. Google Scholar

[15]

Journal of Economic Behavior & Organization, 33 (1998), 143-165. doi: 10.1016/S0167-2681(97)00088-7.  Google Scholar

[16]

International Journal of Theoretical and Applied Finance, 3 (2000), 675-702. doi: 10.1142/S0219024900000826.  Google Scholar

[17]

Nature, 397 (1999), 498-500. Google Scholar

[18]

Physica A, 391 (2012), 715-730. doi: 10.1016/j.physa.2011.08.013.  Google Scholar

[19]

Cambridge University Press, Cambridge, 2007.  Google Scholar

[20]

J. Stat. Phys., 130 (2008), 1087-1117. doi: 10.1007/s10955-007-9462-2.  Google Scholar

[21]

Birkhäuser, Boston, 2010. doi: 10.1007/978-0-8176-4946-3.  Google Scholar

[22]

Oxford University Press, Oxford, 2014. Google Scholar

[23]

Phil. Trans. R. Soc. A, 372 (2014), 20130396, 15pp. doi: 10.1098/rsta.2013.0396.  Google Scholar

[24]

Phys. Rev. E, 69 (2004), 046102. doi: 10.1103/PhysRevE.69.046102.  Google Scholar

[25]

Comm. Math. Scie., 4 (2006), 481-496. doi: 10.4310/CMS.2006.v4.n3.a1.  Google Scholar

[26]

Springer Verlag, Berlin, 2005.  Google Scholar

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