Price and Wealth Dynamics in a Speculative Market with an Arbitrary Number of Generic Technical Traders
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. The general case is studied in which an arbitrary large number of heterogeneous traders operates in the market and any smooth function which maps the infinite information set to the present investment choice is allowed as agent's trading behavior. A complete characterization of equilibria is given and their stability conditions are derived. We find that this economy 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. We show that irrespectively of agents number and of their behavior, all possible equilibria belong to a one dimensional "Equilibria Market Line". Finally we discuss the relative performances of different strategies and the selection principle governing market dynamics.
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