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Change of measure up to a random time: Details

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  • Dorte Kreher

Abstract

This paper extends results of Mortimer and Williams (1991) about changes of probability measure up to a random time under the assumptions that all martingales are continuous and that the random time avoids stopping times. We consider locally absolutely continuous measure changes up to a random time, changes of probability measure up to and after an honest time, and changes of probability measure up to a pseudo-stopping time. Moreover, we apply our results to construct a change of probability measure that is equivalent to the enlargement formula and to build for a certain class of pseudo-stopping times a class of measure changes that preserve the pseudo-stopping time property. Furthermore, we study for a price process modeled by a continuous semimartingale the stability of the No Free Lunch with Vanishing Risk (NFLVR) property up to a random time, that avoids stopping times, in the progressively enlarged filtration and provide sufficient conditions for this stability in terms of the Az\'ema supermartingale.

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  • Dorte Kreher, 2013. "Change of measure up to a random time: Details," Papers 1309.6141, arXiv.org, revised Aug 2016.
    • Handle: RePEc:arx:papers:1309.6141
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    References listed on IDEAS

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    1. Claudio Fontana & Monique Jeanblanc & Shiqi Song, 2012. "On arbitrages arising from honest times," Papers 1207.1759, arXiv.org, revised Jul 2013.
    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.
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    Cited by:

    1. Karen Grigorian & Robert A. Jarrow, 2023. "Enlargement of Filtrations: An Exposition of Core Ideas with Financial Examples," Papers 2303.03573, arXiv.org.

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