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

Quantitative Finance Research Centre, University of Technology, Sydney, Research Paper Number 263

12 Pages Posted: 3 Nov 2012

See all articles by Hardy Hulley

Hardy Hulley

University of Technology, Sydney (UTS) - Finance Discipline Group; Financial Research Network (FIRN)

Eckhard Platen

University of Technology, Sydney (UTS) - Finance Discipline Group; University of Technology Sydney, School of Mathematical and Physical Sciences; Financial Research Network (FIRN)

Date Written: November 1, 2009

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

Suggested Citation

Hulley, Hardy and Platen, Eckhard, A Visual Criterion for Identifying Ito Diffusions as Martingales or Strict Local Martingales (November 1, 2009). Quantitative Finance Research Centre, University of Technology, Sydney, Research Paper Number 263, Available at SSRN: https://ssrn.com/abstract=2170276 or http://dx.doi.org/10.2139/ssrn.2170276

Hardy Hulley

University of Technology, Sydney (UTS) - Finance Discipline Group ( email )

Haymarket
Sydney, NSW 2007
Australia

Financial Research Network (FIRN)

C/- University of Queensland Business School
St Lucia, 4071 Brisbane
Queensland
Australia

HOME PAGE: http://www.firn.org.au

Eckhard Platen (Contact Author)

University of Technology, Sydney (UTS) - Finance Discipline Group ( email )

Broadway
GPO Box 123
Sydney, NSW 2007, 2007
Australia
+61 2 9514 7759 (Phone)

HOME PAGE: http://datasearch.uts.edu.au/business/finance/staff/StaffDetails.cfm?UnitStaffId=90

University of Technology Sydney, School of Mathematical and Physical Sciences ( email )

P.O. Box 123
Broadway
Sydney, New South Wales 2007
Australia
+61 (02) 9514 2271 (Phone)

Financial Research Network (FIRN)

C/- University of Queensland Business School
St Lucia, 4071 Brisbane
Queensland
Australia

HOME PAGE: http://www.firn.org.au

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