Entropy, Bifurcation and Dynamic Market Disequilibrium

Abstract

The study of security market behavior in recent years has focused on the dynamic process of disseminating information throughout the marketplace. Lags in information dissemination and the subsequent market disequilibrium are stressed by many studies in the finance literature [12,3,5,9,10,19,20,29]. While these studies are exciting because of their stress on disequilibrium processes, they are constrained by a standard assumption of stationary stochastic processes [19, footnote 2].The relaxation of this assumption should help to enrich our understanding of disequilibrium processes. Work with chemical processes by Nicolis and Prigogine [33] has relaxed the stationary stochastic process assumption, thereby increasing our knowledge of the evolution of dynamic systems. The major tools used by Nicolis and Prigogine are entropy theory and bifurcation theory. Bifurcation theory is concerned with the restructuring of systems in order to ensure their survival. A bifurcation point is the threshold where the system is restructured. Through the use of bifurcation theory, entropy models can model dynamic processes that change their information structure or their physical structure in response to stress created by disequilibrium conditions, thereby providing a description of nonstationary processes.The application of evolutionary theory to economic processes is strongly defended by Boulding [6,7]. In addition, Majthay [26] provides a strong case for using bifurcation theory instead of the currently popular catastrophe theory [23,38,39]. However, while the use of entropy theory and bifurcation theory is known in the finance and economics literature, [6,12,17,24,26,30,36], these theories have not been used to describe security market disequilibrium.The purposes of this paper are to survey the work in financial market disequilibrium and to describe an application of entropy and bifurcation theories to financial market disequilibrium.The structure of the paper is as follows. First, current models of financial market disequilibrium are described. Next, the work of Nicolis and Prigogine [33] with entropy arid bifurcation models is discussed, along with the application of this work to financial market disequilibrium. Finally, some implications of the entropy model are explored.

Dynamic behavior of a nonlinear macro-financial system

“…A bifurcation in a financial or economic system is defined as a point or threshold where the system is restructured to operate at a more acceptable or stable level of disequilibrium. Bifurcations do not usually lead to equilibrium conditions, only to a stable or comfortable disequilibrium condition under which the system can continue to survive [19]. For a financial system, there can be disequilibrium thresholds where society decides it cannot afford the increasing cost of misallocated resources as disequilibrium increases.…”