Abstract
This paper proposes a mathematical model of financial security prices in continuous time with bubbles in which prices may diverge and crash in finite time. Just before the bubbles burst, prices increase super-exponentially. In addition, a discrete-time excess demand model is proposed to provide a micro-foundation for the continuous-time model. The derived discrete-time security price model has the same characteristics as the continuous-time price model and expresses the finite-time singularity. Furthermore, based on the excess demand model, an agent-based simulation is performed to check the price behavior. As expected, we can confirm that prices can diverge in finite time and increase super-exponentially.
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