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