A SIMPLE MODEL FOR THE NONEQUILIBRIUM DYNAMICS AND EVOLUTION OF A FINANCIAL MARKET

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Abstract
By developing a simple model for market making, price formation can be studied in a nonequilibrium setting. Commonly used trading strategies, such as value investing based on fundamentals, or technical trading based on past price history, generate characteristic price dynamics, including excess volatility, clustered volatility, and long tails. The long term evolution of capital in the market can be modeled in terms of reinvestment of profits, which when combined with the price formation rule leads to generalized Lotka–Volterra equations, originally developed to model predator-prey systems in ecology. Sensible estimates of the characteristic time for substantial capital reallocations are years to decades, suggesting that the progression toward market efficiency may be rather slow.