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In this paper we develop a stochastic analysis for marked binomial processes,that can be viewed as the discrete analogues of marked Poisson processes. Thestarting point is the statement of a chaotic expansion for square-integrable(marked binomial) functionals, prior to the elaboration of a Markov-Malliavinstructure within this framework. We take advantage of the new formalism to dealwith two main applications. First, we revisit the Chen-Stein method for the(compound) Poisson approximation which we perform in the paradigm of the builtMarkov-Malliavin structure, before studying in the second one the problem ofportfolio optimisation in the trinomial model.

Malliavin calculus for marked binomial processes: portfolio optimisation in the trinomial model and compound Poisson approximation