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Article overview
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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 | Abstract: | We 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 | Services: | Forum | Review | PDF | Favorites |
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