Stability Analysis of Asset Flow Differential Equations

Abstract

I study the stability analysis of the solutions for the dynamical system of nonlinear asset flow differential equations (AFDEs) in three versions. I show that the previous two versions are not structurally stable mathematically because there are infinitely many critical points. It is important to reformulate a problem in order to eliminate any hypersensitivity in the mathematical model. I find that there is no critical point in the new version unless the chronic discount over the past finite time interval is zero.

Keywords: Stability analysis, instability, equilibrium, market dynamics, asset flow, closed-end funds, hypersensitivity, mathematical finance and economics

JEL Classification: C62, C61, G12, D52, D53, C63