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A Note on a Paper by Wong and Heyde

Part of: Markov processes Stochastic analysis Stochastic processes

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: [email protected]
∗∗ Postal address: Institute of Mathematical Finance, Ulm University, Ulm 89081, Germany. Email address: [email protected]
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Abstract

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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 parameter 60G48: Generalizations of martingales 60H10: Stochastic ordinary differential equations 60J60: Diffusion processes
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