Flint, Ian; Torrisi, Giovanni Luca A Clark-Ocone formula for temporal point processes and applications. (English) Zbl 1412.60070 Ann. Probab. 45, No. 5, 3266-3292 (2017). Summary: 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. Cited in 1 ReviewCited in 1 Document MSC: 60G55 Point processes (e.g., Poisson, Cox, Hawkes processes) 60H07 Stochastic calculus of variations and the Malliavin calculus Keywords:Clark-Ocone formula; point processes; Malliavin calculus; conditional intensity; deviation inequalities; option hedging PDF BibTeX XML Cite \textit{I. Flint} and \textit{G. L. Torrisi}, Ann. Probab. 45, No. 5, 3266--3292 (2017; Zbl 1412.60070) Full Text: DOI Euclid OpenURL