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September 2017 A Clark–Ocone formula for temporal point processes and applications
Ian Flint, Giovanni Luca Torrisi
Ann. Probab. 45(5): 3266-3292 (September 2017). DOI: 10.1214/16-AOP1136

Abstract

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.

Citation

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Ian Flint. Giovanni Luca Torrisi. "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

Information

Received: 1 October 2015; Revised: 1 May 2016; Published: September 2017
First available in Project Euclid: 23 September 2017

zbMATH: 06812205
MathSciNet: MR3706743
Digital Object Identifier: 10.1214/16-AOP1136

Subjects:
Primary: 60G55, 60H07

Rights: Copyright © 2017 Institute of Mathematical Statistics

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Vol.45 • No. 5 • September 2017
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