Hostname: page-component-7b7567c8c-fvjsw Total loading time: 0 Render date: 2026-11-15T19:18:35.512Z Has data issue: false hasContentIssue false
  • English
  • Français

A Note on a Paper by Wong and Heyde

Part of:Stochastic processesMarkov processesStochastic analysis

Published online by Cambridge University Press:  14 July 2016

Aleksandar Mijatović and
Mikhail Urusov
Aleksandar Mijatović*
Affiliation:
University of Warwick
Mikhail Urusov*
Affiliation:
Ulm University
*
∗ Postal address: Department of Statistics, University of Warwick, Coventry CV4 7AL, UK. Email address: a.mijatovic@warwick.ac.uk
∗∗ Postal address: Institute of Mathematical Finance, Ulm University, Ulm 89081, Germany. Email address: mikhail.urusov@uni-ulm.de
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the 'Save PDF' action button.

In this note we re-examine the analysis of the paper ‘On the martingale property of stochastic exponentials’ by Wong and Heyde (2004). Some counterexamples are presented and alternative formulations are discussed.

Keywords

Local martingales versus true martingalesstochastic exponential

MSC classification

Secondary:60G44: Martingales with continuous parameter60G48: Generalizations of martingales60H10: Stochastic ordinary differential equations60J60: Diffusion processes

Information

Type
Research Papers
Information
Journal of Applied Probability , Volume 48 , Issue 3 , September 2011, pp. 811 - 819
Copyright
Copyright © Applied Probability Trust 2011 

References

[1] Karatzas, I. and Shreve, S. E. (1991). Brownian Motion and Stochastic Calculus (Graduate Texts Math. 113), 2nd edn. Springer, New York.Google Scholar
[2] Mijatović, A. and Urusov, M. (2010). Deterministic criteria for the absence of arbitrage in one-dimensional diffusion models. To appear in Finance Stoch.Google Scholar
[3] Mijatović, A. and Urusov, M. (2010). On the martingale property of certain local martingales. To appear in Prob. Theory Relat. Fields. Google Scholar
[4] Revuz, D. and Yor, M. (1999). Continuous Martingales and Brownian Motion (Fundamental Principles Math. Sci. 293), 3rd edn. Springer, Berlin.Google Scholar
[5] Wong, B. and Heyde, C. C. (2004). On the martingale property of stochastic exponentials. J. Appl. Prob. 41, 654–664.Google Scholar