A traditional model for financial asset prices is that of a solution of a stochastic differential equation, driven by Brownian motion and Lebesgue measure; that is, a standard diffusion. The classic Black-Scholes model is a special case of this rubric. In some situations, however, such a model is...

We study strict local martingales via h-transforms, a method which first appeared in Delbaen-Schachermayer. We show that strict local martingales arise whenever there is a consistent family of change of measures where the two measures are not equivalent to one another. Several old and new strict...

This paper provides an alternative approach to Duffie and Lando [Econometrica 69 (2001) 633-664] for obtaining a reduced form credit risk model from a structural model. Duffie and Lando obtain a reduced form model by constructing an economy where the market sees the manager's information set...

Recent academic work has developed a method to determine, in real time, if a given stock is exhibiting a price bubble. Currently there is speculation in the financial press concerning the existence of a price bubble in the aftermath of the recent IPO of LinkedIn. We analyze stock price tick data...

A strict local martingale is a local martingale which is not a martingale. There are few explicit examples of "naturally occurring" strict local martingales with jumps available in the literature. The purpose of this paper is to provide such examples, and to illustrate how they might arise via...

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 presents an arbitrage-free valuation model for a credit risky security where credit risk coexists and interacts with an asset price bubble and liquidity risk (or liquidity costs). As an illustration, this model is applied to determine the fair rate for microfinance loans

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...