  In an incomplete market underpinned by the trinomial model, we consider two
investors : an ordinary agent whose decisions are driven by public information
and an insider who possesses from the beginning a surplus of information
encoded through a random variable for which he or she knows the outcome.
Through the definition of an auxiliary model based on a marked binomial
process, we handle the trinomial model as a volatility one, and use the
stochastic analysis and Malliavin calculus toolboxes available in that context.
In particular, we connect the information drift, the drift to eliminate in
order to preserve the martingale property within an initial enlargement of
filtration in terms of the Malliavin derivative. We solve explicitly the agent
and the insider expected logarithmic utility maximisation problems and provide
a hedging formula for replicable claims. We identify the insider expected
additional utility with the Shannon entropy of the extra information, and
examine then the existence of arbitrage opportunities for the insider.
