Open AccessAsset price bubbles: Invariance theorems
Author(s) -
Robert A. Jarrow,
Philip Protter,
Jaime San Martı́n
Publication year - 2022
Publication title -
frontiers of mathematical finance
Language(s) - English
Resource type - Journals
ISSN - 2769-6715
DOI - 10.3934/fmf.2021006
Subject(s) - martingale (probability theory) , local martingale , econometrics , quadratic variation , volatility (finance) , martingale pricing , mathematics , markov process , forward price , risk neutral measure , mathematical economics , economics , statistics , brownian motion
This paper provides invariance theorems that facilitate testing for the existence of an asset price bubble in a market where the price evolves as a Markov diffusion process. The test involves only the properties of the price process' quadratic variation under the statistical probability. It does not require an estimate of either the equivalent local martingale measure or the asset's drift. To augment its use, a new family of stochastic volatility price processes is also provided where the processes' strict local martingale behavior can be characterized.