Strong Bubbles and Strict Local Martingales

Abstract

In a numéraire-independent framework, we study a financial market with N assets which are all treated in a symmetric way. We define the fundamental value *S of an asset S as its superreplication price and say that the market has a strong bubble if *S and S 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 numéraires 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.

Note: This paper is a thoroughly revised and rewritten version of an earlier preprint which circulated under the title ”Economics-Based Financial Bubbles (and Why They Imply Strict Local Martingales)“.

Keywords: financial bubble, incomplete financial market, fundamental value, superreplication, strict local martingale, numéraire, viability, efficiency, no dominance efficiency, no dominance

JEL Classification: G10, C60