Price and Wealth Dynamics in a Speculative Market with an Arbitrary Number of Generic Technical Trading Strategies

We consider a simple pure exchange economy with two assets, one riskless, yielding a constant return, and one risky, paying a stochastic dividend, and we assume trading to take place in discrete time inside an endogenous price formation setting. Traders demand for the risky asset is expressed as a fraction of their individual wealth and is based on future prices forecast obtained on the basis of past market history. We describe the evolution of price and wealth distribution in the general case where any number of heterogeneous traders is allowed to operate in the market and any smooth function which maps the infinite information set to the present investment choice is allowed as agent's trading strategy. We give a complete characterization of equilibria and derive stability conditions analyzing a dynamical system of arbitrary large dimension. We show that this system can only possess isolated generic equilibria where a single agent dominates the market and continuous manifolds of non-generic equilibria where many agents hold finite wealth shares. Irrespectively of agents number and of their behavior, we show that all possible equilibria returns belong to a one dimensional ``Equilibria Market Line''. Our general result extends previous contributions and allows a better understanding of the selection principle governing the asymptotic market dynamicsAsset pricing, Price and wealth dynamics, Optimal selection principle.