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Kinetic and Related Models (KRM)
 

A mathematical model for value estimation with public information and herding

Pages: 29 - 44, Volume 7, Issue 1, March 2014      doi:10.3934/krm.2014.7.29

 
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Marcello Delitala - Department of Mathematical Sciences, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy (email)
Tommaso Lorenzi - Department of Mathematical Sciences, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy (email)

Abstract: This paper deals with a class of integro-differential equations modeling the dynamics of a market where agents estimate the value of a given traded good. Two basic mechanisms are assumed to concur in value estimation: interactions between agents and sources of public information and herding phenomena. A general well-posedness result is established for the initial value problem linked to the model and the asymptotic behavior in time of the related solution is characterized for some general parameter settings, which mimic different economic scenarios. Analytical results are illustrated by means of numerical simulations and lead us to conclude that, in spite of its oversimplified nature, this model is able to reproduce some emerging behaviors proper of the system under consideration. In particular, consistently with experimental evidence, the obtained results suggest that if agents are highly confident in the product, imitative and scarcely rational behaviors may lead to an over-exponential rise of the value estimated by the market, paving the way to the formation of economic bubbles.

Keywords:  Socio-economic systems, emerging behaviors, asymptotic analysis, weak convergence, integro-differential equations.
Mathematics Subject Classification:  Primary: 35R09, 91D10; Secondary: 35B40.

Received: November 2012;      Revised: April 2013;      Available Online: December 2013.

 References