Functional It\^o calculus and martingale representation formula for integer-valued measures

  title={Functional It\^o calculus and martingale representation formula for integer-valued measures},
  author={Pierre M. Blacque-Florentin and Rama Cont},
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… CONTINUE READING


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