Random times and multiplicative systems

Libo Li and Marek Rutkowski

Stochastic Processes and their Applications, 2012, vol. 122, issue 5, 2053-2077

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.

Keywords: Random time; Azéma supermartingale; Multiplicative system (search for similar items in EconPapers)
Date: 2012
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Citations: View citations in EconPapers (5)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:122:y:2012:i:5:p:2053-2077

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DOI: 10.1016/j.spa.2012.02.011

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