A Clark–Ocone formula for temporal point processes and applications

• Ian Flint ^[1] ; Giovanni Luca Torrisi
  1. [1] Nanyang Technolopical University (Singapore)
• Localización: Annals of probability: An official journal of the Institute of Mathematical Statistics, ISSN 0091-1798, Vol. 45, Nº. 5, 2017, págs. 3266-3292
• Idioma: inglés
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• Resumen

  • We provide a Clark–Ocone formula for square-integrable functionals of a general temporal point process satisfying only a mild moment condition, generalizing known results on the Poisson space. Some classical applications are given, namely a deviation bound and the construction of a hedging portfolio in a pure-jump market model. As a more modern application, we provide a bound on the total variation distance between two temporal point processes, improving in some sense a recent result in this direction.