Journal of Applied Probability

A note on a paper by Wong and Heyde

Aleksandar Mijatović and Mikhail Urusov

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Abstract

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.

Article information

Source
J. Appl. Probab., Volume 48, Number 3 (2011), 811-819.

Dates
First available in Project Euclid: 23 September 2011

Permanent link to this document
https://projecteuclid.org/euclid.jap/1316796916

Digital Object Identifier
doi:10.1239/jap/1316796916

Mathematical Reviews number (MathSciNet)
MR2884817

Zentralblatt MATH identifier
1237.60033

Subjects
Primary: 60G44: Martingales with continuous parameter 60G48: Generalizations of martingales 60H10: Stochastic ordinary differential equations [See also 34F05] 60J60: Diffusion processes [See also 58J65]

Keywords
Local martingales versus true martingales stochastic exponential

Citation

Mijatović, Aleksandar; Urusov, Mikhail. A note on a paper by Wong and Heyde. J. Appl. Probab. 48 (2011), no. 3, 811--819. doi:10.1239/jap/1316796916. https://projecteuclid.org/euclid.jap/1316796916


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References

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