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.
Mathematics Subject Classification (2000). Primary: 60J60, 60G44; Secondary: 60G40, 60J35, 60J50, 65L99.
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Hulley, H., Platen, E. (2011). A Visual Criterion for Identifying Itô Diffusions as Martingales or Strict Local Martingales. In: Dalang, R., Dozzi, M., Russo, F. (eds) Seminar on Stochastic Analysis, Random Fields and Applications VI. Progress in Probability, vol 63. Springer, Basel. https://doi.org/10.1007/978-3-0348-0021-1_9
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DOI: https://doi.org/10.1007/978-3-0348-0021-1_9
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