Modeling Asymmetric Interactions in Economy

We consider a general nonlinear kinetic type equation that can describe the time evolution of a variable related to an economical state of an individual agent of the system. We assume asymmetric interactions between the agents. We show that in a corresponding limit, it is asymptotically equivalent to a nonlinear inviscid Burgers type equation.

[1]  Juan Soler,et al.  ON THE MATHEMATICAL THEORY OF THE DYNAMICS OF SWARMS VIEWED AS COMPLEX SYSTEMS , 2012 .

[2]  M. Stoll,et al.  Bifurcation analysis of an orientational aggregation model , 2003, Journal of mathematical biology.

[3]  G. Henkin.  Burgers type equations, Gelfand’s problem and Schumpeterian dynamics , 2012 .

[4]  E. Stein,et al.  Stock Price Distributions with Stochastic Volatility: An Analytic Approach , 1991 .

[5]  Henryk Leszczynski,et al.  Diffusive and Anti-Diffusive Behavior for Kinetic Models of Opinion Dynamics , 2019, Symmetry.

[6]  Martin Parisot,et al.  Blow-up and global existence for a kinetic equation of swarm formation , 2017 .

[7]  M. Lachowicz,et al.  A Kinetic Model for the formation of Swarms with nonlinear interactions , 2015 .

[8]  Tyll Krüger,et al.  Conformity, Anticonformity and Polarization of Opinions: Insights from a Mathematical Model of Opinion Dynamics , 2016, Entropy.

[9]  Patryk Siedlecki,et al.  The Interplay Between Conformity and Anticonformity and its Polarizing Effect on Society , 2016, J. Artif. Soc. Soc. Simul..

[10]  Nicola Bellomo,et al.  On the interplay between behavioral dynamics and social interactions in human crowds , 2017, Kinetic & Related Models.

[11]  Nicola Bellomo,et al.  Stochastic Evolving Differential Games Toward a Systems Theory of Behavioral Social Dynamics , 2015, 1506.05699.

[12]  Wei Yang,et al.  Pricing CDO tranches in an intensity based model with the mean reversion approach , 2010, Math. Comput. Model..

[13]  Mirosław Lachowicz,et al.  Individually-based Markov processes modeling nonlinear systems in mathematical biology , 2011 .

[14]  B. Perthame,et al.  Mathematik in den Naturwissenschaften Leipzig An Integro-Differential Equation Model for Alignment and Orientational Aggregation , 2007 .

[15]  Marina Dolfin,et al.  Forecasting Efficient Risk/Return Frontier for Equity Risk with a KTAP Approach - A Case Study in Milan Stock Exchange , 2019, Symmetry.

[16]  H. Othmer,et al.  Models of dispersal in biological systems , 1988, Journal of mathematical biology.

[17]  S. Hodges,et al.  Quasi Mean Reversion in an Efficient Stock Market: The Characterisation of Economic Equilibria which Support Black-Scholes Option Pricing , 1993 .

[18]  M. Dixon,et al.  “Quantum Equilibrium-Disequilibrium”: Asset price dynamics, symmetry breaking, and defaults as dissipative instantons , 2020 .

[19]  Martin Parisot,et al.  A simple kinetic equation of swarm formation: Blow-up and global existence , 2016, Appl. Math. Lett..

[20]  Miroslaw Lachowicz,et al.  Self-organization with small range interactions: Equilibria and creation of bipolarity , 2019, Appl. Math. Comput..

[21]  Jacek Banasiak,et al.  On a macroscopic limit of a kinetic model of alignment , 2012, 1207.2643.

[22]  George A. Akerlof.  The Market for “Lemons”: Quality Uncertainty and the Market Mechanism , 1970 .

[23]  Kiyoshi Asano,et al.  The Euler limit and initial layer of the nonlinear Boltzmann equation , 1983 .