A model of cycles and bubbles under heterogeneous beliefs in financial markets

I study the effect of heterogeneous beliefs about asset prices on the long-term behavior of financial markets. Starting from the ideas of Abreu and Brunnermeier (2003), a two-dimensional system of differential equations is developed. The first dynamic variable is the asset price growth rate. The second dynamic variable is the number of investors who believe that asset prices are abnormally high. In a phase plane analysis, I find both stable and unstable equilibria, depending on the spread of information and the response to other agents' beliefs. If individuals try to increase their returns while perceiving more overpricing, these equilibria can be spirals or even approach limit cycles. Although I intend to study general price patterns, abnormally high asset prices can be caused by financial bubbles. In this model, bubbles can emerge and deflate both in cycles or directly, or they can grow until they burst. Further, I analyze market behavior after a central bank increases the interest rate. This can lead to new stable equilibria, but the emergence and bursting of bubbles cannot be prevented.