Bulg. J. Phys. vol.27 no.S3 (2000), pp. 110-119

Dissipative Structures in the Stock Market Space

M. Gligor, M. Ignat
Abstract. Using the nonequilibrium thermodynamically methods, we analyze the formation and propagation of patterns in the interdealer broker market, the spatial coordinate being the market price, in function of which the spectrum ∅ of deals is modeled. A distributed active medium such as the stock market can be viewed as a set of active elements (traders, brokers) interacting among each other through transactions (typically a diffusion process). The model used is the reaction-diffusion model. The reactive part of the reaction-diffusion equation can be developped from a hot-spot mechanism with a characteristic jump when ∅ pass through ∅C (a critical value). Solving the stationary equation according to Dirichlet boundary conditions, we find two inhomogeneous solutions, both showing that there are "hot deals" regions (meaning the regions of speculative transactions). These can be considered "dissipations" as they no contribute to the gross national product. We prove that from the pair of simultaneous solutions, the one with the larger dissipation is stable, while the other is unstable. The last part is established to the propagation of the patterns processes. A kind of solutions of great interest — the solitary waves — shows the evolution towards the speculative bubbles. These can evolve producing a phase transition to the homogenous states, or the collapse of the dissipative structures. The financial data which illustrate the physical model refer to B.V.B.(Romania), and through references, to New York S.E. and Tokio S.E.

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