In models of financial bubbles, the price of a stock is a priori typically unbounded, and this plays a fundamental role in the analysis of finite horizon local martingale bubbles. It would seem that price bubbles do not apply to bounded risky asset prices, such as bond prices. To avoid this...

This paper provides an invariance theorem that facilitates 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...

After the 2007 credit crisis, nancial bubbles have once again emerged as a topic of current concern. An open problem is to determine in real time whether or not a given asset's price process exhibits a bubble. Due to recent progress in the characterization of asset price bubbles using the...

We provide a new liquidity based model for financial asset price bubbles that explains bubble formation and bubble bursting. The martingale approach (Cox and Hobson (2005), Jarrow et al. (2007)) to modeling price bubbles assumes that the asset's market price process is exogenous and the...

The martingale theory of price bubbles defines an asset bubble to exist when the asset's price process is a strict local martingale, that is, a local martingale that is not a martingale. Using this definition of a price bubble, for continuous semimartingales, we characterize the conditions under...

This paper provides a mathematical analysis of how high frequency traders profi t from their speed with respect to the limit order book. We show that their pro ts can be decomposed into two components. The rest is due to their ability to execute market orders at limit order prices and without...