Price and wealth asymptotic dynamics with CRRA technical trading strategies

We consider a simple pure exchange economy with two assets, one riskless, yielding a constant return on investment, and one risky, paying a stochastic dividend. Trading takes place in discrete time and in each trading period the price of the risky asset is fixed by imposing market clearing condition on the sum of traders individual demand functions. We assume that agents' strategies are consistent with maximizing a CRRA utility, so that the individual demand for the risky asset is expressed as a fraction of the agent's wealth and the evolution of price and wealth distribution is described by means of a dynamical system. We consider agents whose individual demand function is based on future prices forecasts obtained on the basis of past market history and we analyze two cases. First, we consider a large population of quasi-homogeneous agents, whose individual choices can be described as a random deviation from an underlying, common, behavior. We denote the particular dynamics that emerges as Large Market Limit and, with the help of numerical simulations, we provide some hints on the range of its applications. As an example of application of the Large Market Limit we show how the results in Chiarella and He (2001) concerning models with optimizing agents can be replicated in our framework. Next, we analyze the case of two agents with distinct, but generic, investment strategies. We study the set of equilibria allowed by the two strategies and provide an asymptotic characterization of their relative performances. We find that the market endogenously selects the dominant trader among the participants following a quasi-optimal selection principle. The same principle, however, implies the impossibility of defining a dominance order relation on the space of strategies.