Generalized Lotka-Volterra (GLV) Models and Generic Emergence of Scaling Laws in Stock Markets

Details Generalized Lotka-Volterra (GLV) Models and Generic Emergence of Scaling Laws in Stock Markets Generalized Lotka-Volterra (GLV) Models and Generic Emergence of Scaling Laws in Stock Markets

1999-01-23

arxiv.org/abs/cond-mat/9901250v1

Physics

Condensed Matter

To appear in Econophysics Budapest 1997, (Kluver Academic Press), eds. Imre Kondor and Janos Kertes

Scientific paper

This is a pedagogical review of the the Generalized Lotka-Volterra (GLV) model: w_i(t+1) = lambda * w_i(t) + a * W (t) - c * W (t) * w_i(t) where i=1, >......, N and W= (w_1 + w_2 + ...w_N)/N is the average of the w_i's. The GLV models provide a generic method to simulate, analyze and understand a wide class of phenomena which are characterized by (truncated) power-law probability distributions: P(w) dw ~ w**(-1 -alpha) dw and (truncated) Levy flights fluctuations L_alpha (W). The implications and the interpretation of the model in the stock markets are discussed.

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