Generalized Lotka-Volterra (GLV) Models and Generic Emergence of Scaling Laws in Stock Markets
Abstract
This is a pedagogical review of the the Generalized Lotka-Volterra (GLV) model: wi(t+1) = lambda * wi(t) + a * W (t) - c * W (t) * wi(t) where i=1, >......, N and W= (w1 + w2 + ...wN)/N is the average of the wi'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 Lalpha (W). The implications and the interpretation of the model in the stock markets are discussed.
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