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Non-stopping times and stopping theorems

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  • Nikeghbali, Ashkan

Abstract

Given a random time, we give some characterizations of the set of martingales for which the stopping theorems still hold. We also investigate how the stopping theorems are modified when we consider arbitrary random times. To this end, we introduce some families of martingales with remarkable properties.

Suggested Citation

  • Nikeghbali, Ashkan, 2007. "Non-stopping times and stopping theorems," Stochastic Processes and their Applications, Elsevier, vol. 117(4), pages 457-475, April.
    • Handle: RePEc:eee:spapps:v:117:y:2007:i:4:p:457-475
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    References listed on IDEAS

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    1. R. J. Elliott & M. Jeanblanc & M. Yor, 2000. "On Models of Default Risk," Mathematical Finance, Wiley Blackwell, vol. 10(2), pages 179-195, April.
    2. Nikeghbali, Ashkan, 2006. "A class of remarkable submartingales," Stochastic Processes and their Applications, Elsevier, vol. 116(6), pages 917-938, June.
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    Cited by:

    1. Nikeghbali, Ashkan, 2008. "How badly are the Burkholder-Davis-Gundy inequalities affected by arbitrary random times?," Statistics & Probability Letters, Elsevier, vol. 78(6), pages 766-770, April.
    2. Delia Coculescu & Monique Jeanblanc & Ashkan Nikeghbali, 2012. "Default times, no-arbitrage conditions and changes of probability measures," Finance and Stochastics, Springer, vol. 16(3), pages 513-535, July.
    3. Delia Coculescu, 2009. "From the decompositions of a stopping time to risk premium decompositions," Papers 0912.4312, arXiv.org, revised May 2010.

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