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.
"A Clark–Ocone formula for temporal point processes and applications." Ann. Probab. 45 (5) 3266 - 3292, September 2017. https://doi.org/10.1214/16-AOP1136