Bubbles and crashes: Escape dynamics in financial markets

We develop a financial market model focused on fund managers who continuously adjust their exposure to risk in response to the payoff gradient. 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 adopt riskier portfolios. Then slight losses can trigger a crash, as a widening risk premium accelerates the decline in asset price.