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16 February 2025
 
  » arxiv » 1508.0048

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Functional It^o calculus and martingale representation formula for integer-valued measures
Pierre M. Blacque-Florentin ; Rama Cont ;
Date 1 Aug 2015
AbstractWe develop a calculus for functionals of integer-valued measures, which extends the Functional It^o calculus to functionals of Poisson random measures in a pathwise sense. We show that smooth functionals in the sense of this pathwise calculus are dense in the space of square-integrable (compensated) integrals with respect to a large class of integer-valued random measures. As a consequence, we obtain an explicit martingale representation formula for all square-integrable martingales with respect to the filtration generated by such integer-valued random measures. Our representation formula extends beyond the Poisson framework and allows for random and time-dependent compensators.
Source arXiv, 1508.0048
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