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.
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