 Random times with given survival probability and their -martingale decomposition formulaMonique Jeanblanc and Shiqi Song Stochastic Processes and their Applications, 2011, vol. 121, issue 6, 1389-1410 Abstract: Given a filtered probability space , an -adapted continuous increasing process [Lambda] and a positive local martingale N such that satisfies Zt =0, we construct probability measures and a random time [tau] on an extension of , such that the survival probability of [tau], i.e., is equal to Zt for t>=0. We show that there exist several solutions and that an increasing family of martingales, combined with a stochastic differential equation, constitutes a natural way to construct these solutions. Our extended space will be equipped with the enlarged filtration where is the [sigma]-field completed with the -negligible sets. We show that all martingales remain -semimartingales and we give an explicit semimartingale decomposition formula. Finally, we show how this decomposition formula is intimately linked with the stochastic differential equation introduced before. Keywords: Progressive; enlargement; of; filtration; Semimartingale; decomposition; Multiplicative; decomposition; Credit; risk (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:121:y:2011:i:6:p:1389-1410 Ordering information: This journal article can be ordered from Access Statistics for this article Stochastic Processes and their Applications is currently edited by T. Mikosch More articles in Stochastic Processes and their Applications from Elsevier |
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