Random times and multiplicative systems
The present research is motivated by the recent results of Jeanblanc and Song (2011) [10,11]. Our aim is to demonstrate, with the help of multiplicative systems introduced in Meyer (1979) , that for any given positive F-submartingale F such that F∞=1, there exists a random time τ on some extension of the filtered probability space such that the Azéma submartingale associated with τ coincides with F. Pertinent properties of this construction are studied and it is subsequently extended to the case of several correlated random times with the predetermined univariate conditional distributions.
Volume (Year): 122 (2012)
Issue (Month): 5 ()
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Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Jeanblanc, Monique & Song, Shiqi, 2011. "Random times with given survival probability and their -martingale decomposition formula," Stochastic Processes and their Applications, Elsevier, vol. 121(6), pages 1389-1410, June.
- R. J. Elliott & M. Jeanblanc & M. Yor, 2000. "On Models of Default Risk," Mathematical Finance, Wiley Blackwell, vol. 10(2), pages 179-195.
- Kardaras, Constantinos, 2010. "Numéraire-invariant preferences in financial modeling," LSE Research Online Documents on Economics 44993, London School of Economics and Political Science, LSE Library.
- Jeanblanc, Monique & Song, Shiqi, 2011. "An explicit model of default time with given survival probability," Stochastic Processes and their Applications, Elsevier, vol. 121(8), pages 1678-1704, August.
- El Karoui, Nicole & Jeanblanc, Monique & Jiao, Ying, 2010. "What happens after a default: The conditional density approach," Stochastic Processes and their Applications, Elsevier, vol. 120(7), pages 1011-1032, July.
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