A mathematical framework for inefficient market bubbles

Following the understanding that asset price bubbles are generated by market failures, we present a framework for explosive semimartingales that is based on the antagonistic combination of (i) an excessive pre-crash process... [ view full abstract ]

Following the understanding that asset price bubbles are generated by market failures, we present a framework for explosive semimartingales that is based on the antagonistic combination of (i) an excessive pre-crash process and (ii) the random time of a drawdown.

We show that "rational expectation bubbles" are by design afflicted with an inherent error in both continuous ("strict local martingale") and discrete time models.

Our framework significantly extends the range of feasible asset price processes during times of excessive growth. It will simplify and foster interdisciplinary exchange at the intersection of economics and mathematical finance and encourage further research.