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A Clark-Ocone formula for temporal point processes and applications. (English) Zbl 1412.60070

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.

MSC:

60G55 Point processes (e.g., Poisson, Cox, Hawkes processes)
60H07 Stochastic calculus of variations and the Malliavin calculus
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