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A continuous non-Brownian motion martingale with Brownian motion marginal distributions

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  • Albin, J.M.P.

Abstract

We construct a continuous martingale that has the same univariate marginal distributions as Brownian motion, but that is not Brownian motion.

Suggested Citation

  • Albin, J.M.P., 2008. "A continuous non-Brownian motion martingale with Brownian motion marginal distributions," Statistics & Probability Letters, Elsevier, vol. 78(6), pages 682-686, April.
    • Handle: RePEc:eee:stapro:v:78:y:2008:i:6:p:682-686
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    References listed on IDEAS

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    1. John C. Cox & Jonathan E. Ingersoll Jr. & Stephen A. Ross, 2005. "A Theory Of The Term Structure Of Interest Rates," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 5, pages 129-164, World Scientific Publishing Co. Pte. Ltd..
    2. Albin, J. M. P., 1993. "Extremes of diffusions over fixed intervals," Stochastic Processes and their Applications, Elsevier, vol. 48(2), pages 211-235, November.
    3. Luciano Campi, 2004. "Arbitrage and completeness in financial markets with given N-dimensional distributions," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 27(1), pages 57-80, August.
    4. Carr, Peter & Madan, Dilip B., 2005. "A note on sufficient conditions for no arbitrage," Finance Research Letters, Elsevier, vol. 2(3), pages 125-130, September.
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    Cited by:

    1. Mathias Beiglbock & Gudmund Pammer & Walter Schachermayer, 2021. "From Bachelier to Dupire via Optimal Transport," Papers 2106.12395, arXiv.org.
    2. Mathias Beiglböck & Gudmund Pammer & Walter Schachermayer, 2022. "From Bachelier to Dupire via optimal transport," Finance and Stochastics, Springer, vol. 26(1), pages 59-84, January.
    3. Mathias Beiglbock & George Lowther & Gudmund Pammer & Walter Schachermayer, 2021. "Faking Brownian motion with continuous Markov martingales," Papers 2109.12927, arXiv.org.
    4. Baker, David M., 2015. "Quantizations of probability measures and preservation of the convex order," Statistics & Probability Letters, Elsevier, vol. 107(C), pages 280-285.

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