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Random times and multiplicative systems

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  • Li, Libo
  • Rutkowski, Marek

Abstract

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) [21], 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.

Suggested Citation

  • Li, Libo & Rutkowski, Marek, 2012. "Random times and multiplicative systems," Stochastic Processes and their Applications, Elsevier, vol. 122(5), pages 2053-2077.
    • Handle: RePEc:eee:spapps:v:122:y:2012:i:5:p:2053-2077
    DOI: 10.1016/j.spa.2012.02.011
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    References listed on IDEAS

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    1. 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.
    2. R. J. Elliott & M. Jeanblanc & M. Yor, 2000. "On Models of Default Risk," Mathematical Finance, Wiley Blackwell, vol. 10(2), pages 179-195, April.
    3. 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.
    4. 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.
    5. 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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    Cited by:

    1. Cleary, Brendan & Duffy, Aidan & Bach, Bjarne & Vitina, Aisma & O’Connor, Alan & Conlon, Michael, 2016. "Estimating the electricity prices, generation costs and CO2 emissions of large scale wind energy exports from Ireland to Great Britain," Energy Policy, Elsevier, vol. 91(C), pages 38-48.
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    4. Libo Li, 2018. "Characterisation of honest times and optional semimartingales of class-($\Sigma$)," Papers 1801.03873, arXiv.org, revised Dec 2021.
    5. Gapeev, Pavel V. & Jeanblanc, Monique, 2024. "On the construction of conditional probability densities in the Brownian and compound Poisson filtrations," LSE Research Online Documents on Economics 121059, London School of Economics and Political Science, LSE Library.

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