Applying an Endogenized PID Controller Design to Speculative Bubble Formation

Speculative bubble formation has been a feature of markets for nearly 400 years, and continues to be a major focus of economic, marketing, and operations management research. While these bubbles may form because of specific physical or informational features of the markets in which they occur, it is the interplay of current realized prices and future expected rewards, offset by rising risk of loss with increased speculation, that drives the formation of these bubbles. In other words, it is the behavioral features of the individual decision makers more so than the physics of these markets that yield these bubbles. The comparison of a current state of a system with some expected state to minimize resultant distance in terms of instantaneous, forward projected, and cumulative observations is a feature of both this speculative bubble formation and classical control theory as well. This work presents a framework for adding more behaviorally realistic endogeneity into a classical PID controller design and illustrates its use in both modeling a classical speculative bubble and proposing corresponding policies. More practically, this framework can be considered as the basis for a new fundamental molecule of modeling structure for use in similar modeling endeavors