Crashes and Bubbles: a heterogeneous agent model with transaction costs and learning
N Investors trade in a single risky asset over a finite time horizon. Trades are executed at prices observed by all investors. While no investor knows the true dynamics of the execution price process, each investor has developed his own model to forecast its evolution. Every investor updates his views on the realized values of his modelÃ¢ï¿½ï¿½s random parameters via filtering; however, the investors cannot alter the general form of their models. Each investor selects an adapted trading strategy in a suitable class in order to maximize his own objective function according to his beliefs. We show that singularities can occur in the execution price under certain conditions. Intuitively, our key examples can be summarized as follows: (1) A sufficiently gullible investor planning his trades using a sufficiently inaccurate model for a sufficiently long period of time can blow up the market. (2) A sufficient number of sufficiently gullible investors trading for a sufficiently long period of time can blow up the market, regardless of the distribution of initial bullish/bearish outlooks, initial long/short positions, or plans for overall accumulation/liquidation.