# American Institute of Mathematical Sciences

July  2011, 16(1): 109-150. doi: 10.3934/dcdsb.2011.16.109

## Multi-group asset flow equations and stability

 1 Mathematics Department, University of Pittsburgh, Pittsburgh, PA 15260, United States 2 University of Pittsburgh, Department of Mathematics 301 Thackeray Hall, Pittsburgh, PA 15260, United States

Received  April 2010 Revised  June 2010 Published  April 2011

We consider a two-group asset flow model of a financial instrument with one group focused on price trend, the other on value. We prove the existence of both stable and unstable regions for the system of differential equations and show that a strong motivation based on (particularly recent) price trend is associated with instability. Numerical computations using a set of typical parameters describe precise regions of stability and instability. A precise limiting connection between the discrete and differential equations is also established.
Citation: Gunduz Caginalp, Mark DeSantis. Multi-group asset flow equations and stability. Discrete & Continuous Dynamical Systems - B, 2011, 16 (1) : 109-150. doi: 10.3934/dcdsb.2011.16.109
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