Abstract
We develop stochastic analysis tools for marked binomial processes (MBP) that are the discrete analogues of the marked Poisson processes. They include in particular: (i) the statement of a chaos decomposition for square-integrable functionals of MBP, (ii) the design of a tailor-made Malliavin calculus of variations, (iii) the statement of the analogues of Stroock’s, Clark’s and Mehler’s formulas. We provide our formalism with two applications: (App1) studying the (compound) Poisson approximation of MBP functional by combining it with the Chen-Stein method and (App2) solving an optimal hedging problem in the trinomial model.
Funding Statement
This project has received funding from the European Union’s Horizon 2020 research and innovation programme under grant agreement .
Acknowledgments
I am also very grateful to Giovanni Peccati for motivating discussions and for helpful advice on writing, and to Antonin Bourgeois, Valentin Garino and Pierre Perruchaud for their help with language issues.
Citation
Hélène Halconruy. "Malliavin calculus for marked binomial processes and applications." Electron. J. Probab. 27 1 - 39, 2022. https://doi.org/10.1214/22-EJP892
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