MS#121. Bubbles and Crashes: Gradient Dynamics in Financial Markets, 2005 with Dan Friedman, UCSC, Santa Cruz, CA J. Economic Dynamics and Control, 33:4, April 2008: 922-937. Subjects: Economics Written: January 22, 2005 Abstract: Fund managers respond to the payoff gradient by continuously adjusting leverage in our analytic and simulation models. The base model has a stable equilibrium with classic properties. However, bubbles and crashes occur in extended models incorporating an endogenous market risk premium based on investors’ historical losses and constant-gain learning. When losses have been small for a long time, asset prices inflate as fund managers increase leverage. Then slight losses can trigger a crash, as a widening risk premium accelerates deleveraging and asset price declines. [PDF] 37 pages, 792 KB Last revised by Ralph Abraham