Chaos and stability of the financial system

Abstract

Financial stability is one of the most widely discussed issues in today’s economic literature. The relevance of analyses on financial stability was first recognized during the international financial crises at the end of the 90s, also strengthened by the financial and economic crisis emerging in 2007. Even if an economical system possesses deterministic characteristics, a chaotic behavior can occur in the financial system. Because of slight errors, chaotic dynamical systems can lead to completely different trajectories. Hence, the chaos control in the financial systems is required. In this paper, we analyze the stability of equilibria of a financial system described by three dynamic equations and apply stabilization techniques for the unstable equilibrium state of the system. Our results are essentially based on the Theorem of allotting the characteristic polynomial (see, e.g. [1], Theorem 2.2.3). We also suggest the use of optimal stabilization, by means of a quadratic loss-function.