Change-point problems are considered in which at some unobservable time the intensity of a point process switches from one level to another. Optimal detection stopping times are derived for different information levels.

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A model for a financial asset is constructed with two types of agents, who differ in terms of their beliefs. The proportion of the two types changes over time according to stochastic processes which model the interaction between the agents. Agents do not persist in holding “wrong” beliefs and bubble–like phenomena in the asset price occur. We consider tests for detecting bubbles in the conditio...