STRONG BUBBLES AND STRICT LOCAL MARTINGALES

Abstract

In a numéraire-independent framework, we study a financial market with [Formula: see text] assets which are all treated in a symmetric way. We define the fundamental value ∗S of an asset [Formula: see text] as its super-replication price and say that the market has a strong bubble if ∗S and [Formula: see text] deviate from each other. None of these concepts needs any mention of martingales. Our main result then shows that under a weak absence-of-arbitrage assumption (basically NUPBR), a market has a strong bubble if and only if in all numéraire s for which there is an equivalent local martingale measure (ELMM), asset prices are strict local martingales under all possible ELMMs. We show by an example that our bubble concept lies strictly between the existing notions from the literature. We also give an example where asset prices are strict local martingales under one ELMM, but true martingales under another, and we show how our approach can lead naturally to endogenous bubble birth.