A Model of Asset Price Bubbles that Shows Chaotic Dynamics

Vinod Cheriyan, ISYE, (mentor: Anton J. Kleywegt, ISYE; Federico Bonetto, Math) - Price bubbles, crashes, and cycles have occurred repeatedly over the past four centuries, and have been described and studied in many ways. One of the more recent approaches has been to study these phenomena using models with boundedly rational agents. The purpose of our project is to develop a model in which investors behave reasonably, although with imperfect expectations, that attempt to provide insight into the formation of bubbles. In our previous work, it was shown that a very simple model with a single investment asset leads to a two dimensional dynamical system that exhibits complex dynamics. In particular, the system shows a rich set of phenomena including periodic cycles, chaotic and fractal cycles. The goal of the current proposal is to extend the simple, single-asset model to a multi-asset setting. In this setting we try to develop a more complete model of cyclical behavior that incorporates multiple assets, with each cycle being driven by some assets, and other assets’ prices following along. We expect that many of the interesting complex dynamics phenomena will carry over to this more detailed model.