Abstract
This chapter discusses the applications of catastrophe theory in banking and finance. Catastrophe theory investigates the qualitative aspects of discontinuity in natural phenomena. Thom's classification theorem for stable universal unfoldings, the main result in catastrophe theory, provides a better understanding of causes and effects of catastrophic phenomena in many disciplines, including biology, physics, and engineering. The catastrophic phenomena discussed in the chapter have three properties. The first property is that of divergence whereby small, continuous changes in initial conditions (or parameters) can lead to large, discontinuous (catastrophic) changes in state variables. This type of behavior contrasts with traditional, Hamiltonian, dynamic systems in which small changes in initial conditions result in only small changes in the state variable. The second property is that of bifurcation (or asymmetries) in the behavior of a state variable x as certain parameters increase or decrease; bifurcation implies that there will be a discontinuous jump in x at some value of a control variable when it is increasing that is different from the behavior of x when the control variable is decreasing. As a result, x will be multivalued over a certain range of the control variable. The third property is that of stability—the catastrophe condition is robust to marginal changes in the structural relationships underlying the system.
Published Version
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