Doob's maximal identity, multiplicative decompositions and enlargements of filtrations
By Ashkan Nikeghbali, Marc Yor. 2005
84 citations recorded by the source corpus.
In the theory of progressive enlargements of filtrations, the supermartingale $Z_{t}=\mathbf{P}( g>t\mid \mathcal{F}_{t}) $ associated with an honest time $g$, and its additive (Doob-Meyer) decomposition, play an essential role. In this paper, we propose an alternative approach, using a multiplicative representation for the supermartingale $Z_{t}$, based on Doob's maximal identity. We thus give new examples of progressive enlargements. Moreover, we give, in our setting, a proof of the decomposition formula for martingales , using initial enlargement techniques, and use it to obtain some path decompositions given the maximum or minimum of some processes.
Subfields: Finance, Management Science and Operations Research
View Paper: https://www.semanticscholar.org/paper/cb00b9d751a4e4ea33e2f73f9083cafa976bc659
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In Management Science and Operations Research
Citations in the corpus
- A class of remarkable submartingales (2005, methodology): “It plays a key role in martingale theory: the family of Az´ ema-Yor martingales, the resolution of Skorokhod’s embedding problem, the study of Brownian local times (see [25] chapter VI for more references and examples; see also [29], [16], [4], [5], [ 19 ]).”