A Visual Criterion For Identifying Ito Diffusions As Martingalesor Strict Local Martingales

It is often important, in applications of stochastic calculus to financial modeling, to know whether a given local martingale is a martingale or a strict local martingale. The authors address this problem in the context of a time-homogenous diffusion process with a finite lower boundary, presented as the solution of a drift less stochastic differential equation. The main theorem demonstrates that the question of whether or not this process is a martingale may be decided simply by examining the slope of a certain increasing function. Further results establish the connection between the theorem and other results in the literature, while a number of examples are provided to illustrate the use of the criterion.