A Visual Criterion for Identifying Ito Diffusions as Martingales or Strict Local Martingales

Hardy Hulley and Eckhard Platen (eckhard.platen@uts.edu.au)

No 263, Research Paper Series from Quantitative Finance Research Centre, University of Technology, Sydney

Abstract: It is often important, in applications of stochastic calculus to financial modelling, to know whether a given local martingale is a martingale or a strict local martingale. We address this problem in the context of a time-homogenous diffusion process with a finite lower boundary, presented as the solution of a driftless stochastic differential equation. Our 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 our theorem and other results in the literature, while a number of examples are provided to illustrate the use of our criterion.

Keywords: diffusions; first-passage times; Laplace transforms; local martingales; ordinary differential equations (search for similar items in EconPapers)
Pages: 12 pages
Date: 2009-11-01
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Citations: View citations in EconPapers (8)

Published as: Hulley, H. and Platen, E., 2011, "A Visual Criterion for Identifying Ito Diffusions as Martingales or Strict Local Martingales", In: Seminar on Stochastic Analysis, Random Fields and Applications VI, Volume 63 of the series Progress in Probability, 147-157.

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