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Seminar on Stochastic Analysis, Random Fields and Applications VIA Visual Criterion for Identifying Itô Diffusions as Martingales or Strict Local Martingales

Seminar on Stochastic Analysis, Random Fields and Applications VI: A Visual Criterion for... [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.] http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png

Seminar on Stochastic Analysis, Random Fields and Applications VIA Visual Criterion for Identifying Itô Diffusions as Martingales or Strict Local Martingales

Part of the Progress in Probability Book Series (volume 63)
Editors: Dalang, Robert; Dozzi, Marco; Russo, Francesco
Hulley, Hardy; Platen, Eckhard
Seminar on Stochastic Analysis, Random Fields and Applications VI — Feb 4, 2011
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Publisher
Springer Basel
Copyright
© Springer Basel AG 2011
ISBN
978-3-0348-0020-4
Pages
147 –157
DOI
10.1007/978-3-0348-0021-1_9
Publisher site
See Chapter on Publisher Site

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.]

Published: Feb 4, 2011

Keywords: Diffusions; first-passage times; Laplace transforms; local martingales; ordinary differential equations.

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