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A new kind of augmentation of filtrations suitable for a change of probability measure by a strict local martingale

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  • Kreher, Dörte
  • Nikeghbali, Ashkan

Abstract

In this note we introduce a new kind of augmentation of filtrations along a sequence of stopping times. This augmentation is suitable for the construction of new probability measures associated to a positive strict local martingale as done in Kardaras et al. (2015), while it is on the other hand rich enough to make classical results from stochastic analysis hold true on some stochastic interval of interest.

Suggested Citation

  • Kreher, Dörte & Nikeghbali, Ashkan, 2015. "A new kind of augmentation of filtrations suitable for a change of probability measure by a strict local martingale," Statistics & Probability Letters, Elsevier, vol. 104(C), pages 94-101.
    • Handle: RePEc:eee:stapro:v:104:y:2015:i:c:p:94-101
    DOI: 10.1016/j.spl.2015.05.008
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    References listed on IDEAS

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    1. Peter Carr & Travis Fisher & Johannes Ruf, 2014. "On the hedging of options on exploding exchange rates," Finance and Stochastics, Springer, vol. 18(1), pages 115-144, January.
    2. Soumik Pal & Philip Protter, 2007. "Analysis of continuous strict local martingales via h-transforms," Papers 0711.1136, arXiv.org, revised Jun 2010.
    3. Kardaras, Constantinos & Kreher, Dörte & Nikeghbali, Ashkan, 2015. "Strict local martingales and bubbles," LSE Research Online Documents on Economics 64967, London School of Economics and Political Science, LSE Library.
    4. Pal, Soumik & Protter, Philip, 2010. "Analysis of continuous strict local martingales via h-transforms," Stochastic Processes and their Applications, Elsevier, vol. 120(8), pages 1424-1443, August.
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